Soal dan jawaban Anril(analisis real) 2.1 November 30, 2015 1-10 , 2.1 , analisis , anril , anril 1 , bartle , jawaban , pembahasan , sherbert , Soal <div dir="ltr" style="text-align: left;" trbidi="on"><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;">Untuk membantu anda keluar dari jerat kesulitan mengerjakan soal analisis real 1, saya akan membantu dengan postingan soal analisi real 1 yaitu pembahasan soal latihan 2.1 yang terdapat dalam buku karangan Bartle Dan Sherbert. Mari disimak teman-teman. </span></div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><b>Untuk soal no 1</b></span></div><div style="text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-Bu25vYnpjz5zu59hNNVdHERMnRGh-4PQ4QYoPkS_WzuivIoPcfsI2pw6_-05pjzEDRGcEsX4Mrqube-F5e4WQ_IzznzblvxPSDjKNI8vKH2IoX1rwIKWnu58A-f4uovSjd5O0QXqXf0/s1600/soal+no+1+analisis+real+bartle+2.1.jpg"><span style="font-family: "times" , "times new roman" , serif;"><img border="0" height="44" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-Bu25vYnpjz5zu59hNNVdHERMnRGh-4PQ4QYoPkS_WzuivIoPcfsI2pw6_-05pjzEDRGcEsX4Mrqube-F5e4WQ_IzznzblvxPSDjKNI8vKH2IoX1rwIKWnu58A-f4uovSjd5O0QXqXf0/s320/soal+no+1+analisis+real+bartle+2.1.jpg" width="320" /></span></a></div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><i>Untuk pembahasan soal di atas, simak pembahasan di bawah ini:</i></span></div><div style="text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFFoRq5I4dEadIXqWwtyux3ObnACwqhxXkSCoZ_NgIpzYV64IfMYDAozXq_nQspRQ9_xaQmygZQXzETJ5cP3K9I74gDbgtseaHS8DiGgMWHQ02x0h-KvxSieZBz8RQZ7Z_AqIIKGpGjOg/s1600/pembahasan+soal+no+1.jpg"><span style="font-family: "times" , "times new roman" , serif;"><img border="0" height="111" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFFoRq5I4dEadIXqWwtyux3ObnACwqhxXkSCoZ_NgIpzYV64IfMYDAozXq_nQspRQ9_xaQmygZQXzETJ5cP3K9I74gDbgtseaHS8DiGgMWHQ02x0h-KvxSieZBz8RQZ7Z_AqIIKGpGjOg/s400/pembahasan+soal+no+1.jpg" width="400" /></span></a></div><div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;">Baca juga: </span></div></div><div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></div></div><div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><b>Soal no 2</b></span></div></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEic1bkNsmhKsta2cuAw0dBhxGHRxfCDJkGqmnQ5TsOwZ56C8-4HLgXWRiBJ07k2BsG-Hw5qT-gabSyp_lGcR4cZZSf3nuSAE_1Dd-wtid57cZ5zuFUyFzSWvrCLNWD3DSzWgAWf5p6TaKA/s1600/soal+no+2.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><span style="font-family: "times" , "times new roman" , serif;"><img border="0" height="60" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEic1bkNsmhKsta2cuAw0dBhxGHRxfCDJkGqmnQ5TsOwZ56C8-4HLgXWRiBJ07k2BsG-Hw5qT-gabSyp_lGcR4cZZSf3nuSAE_1Dd-wtid57cZ5zuFUyFzSWvrCLNWD3DSzWgAWf5p6TaKA/s320/soal+no+2.jpg" width="320" /></span></a></div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><i>Pembahasan soal no 2</i></span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWcdiJxDVraNIGtz1eKWntX-tNydPB8Auz50Tp3OaggNSSm4OGrc10RdbL0HAFlsIZOtHgcjLkWR9EP-TsWmhDXMM15vwnphtGYunlDPmDhGKqsEhOpDhCOhnNVEqHNXJneY4TCOPPkGM/s1600/pembahasan+soal+no+2.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><span style="font-family: "times" , "times new roman" , serif;"><img border="0" height="101" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWcdiJxDVraNIGtz1eKWntX-tNydPB8Auz50Tp3OaggNSSm4OGrc10RdbL0HAFlsIZOtHgcjLkWR9EP-TsWmhDXMM15vwnphtGYunlDPmDhGKqsEhOpDhCOhnNVEqHNXJneY4TCOPPkGM/s320/pembahasan+soal+no+2.jpg" width="320" /></span></a></div><div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></div></div><div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></div></div><div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></div></div><div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></div></div><div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></div></div><div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></div></div><div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><b>soal no 4,5</b></span></div></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUfl0_GDv_whgt5sPf3Q692_mh3pehx9pY9-yvLcI5xTLDV6X3ynHhytHCwiOdb5RH91N2hRUSGYgVRwGgKcWQVeaYhSXhs9PfNmJsm-JXFNEJKcW_CPovQraZiLXjD-yuqJSYZuSS1Js/s1600/soal+4%252C5.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><span style="font-family: "times" , "times new roman" , serif;"><img border="0" height="63" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUfl0_GDv_whgt5sPf3Q692_mh3pehx9pY9-yvLcI5xTLDV6X3ynHhytHCwiOdb5RH91N2hRUSGYgVRwGgKcWQVeaYhSXhs9PfNmJsm-JXFNEJKcW_CPovQraZiLXjD-yuqJSYZuSS1Js/s400/soal+4%252C5.jpg" width="400" /></span></a></div><div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></div></div><div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></div></div><div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></div></div><div><div style="text-align: justify;"><br /><i><br /></i></div></div><div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><i>pembahasan soal no 4,5</i></span></div></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6S0yy68tVm4H9acOtgu53NZuHKzdrWgZ2kRR94wN6trwhxp67fFwzhJr15wekTLECUWeM58Hl1M04n5DCFeEDncvezFkqXiw_AsZ4GFTY4b5gOMsLEwjNXE6fWxBpbUakKScH3SrHeXs/s1600/jawaban+4%252C5.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><span style="font-family: "times" , "times new roman" , serif;"><img border="0" height="80" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6S0yy68tVm4H9acOtgu53NZuHKzdrWgZ2kRR94wN6trwhxp67fFwzhJr15wekTLECUWeM58Hl1M04n5DCFeEDncvezFkqXiw_AsZ4GFTY4b5gOMsLEwjNXE6fWxBpbUakKScH3SrHeXs/s400/jawaban+4%252C5.jpg" width="400" /></span></a></div><div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></div></div><div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></div></div><div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></div></div><div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></div></div><div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></div></div><div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></div></div><div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><br /></span></div></div><div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><b>soal no 6 </b></span></div></div><div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;">6). Buktikan bahwa tidak ada bilangan rasional s yang memenuhi s<sup>2</sup> = 6</span><br /><span style="font-family: "times" , "times new roman" , serif;"><br /></span></div></div><div class="MsoNormal"><span style="font-family: "times" , "times new roman" , serif;"><o:p></o:p></span></div><div><div style="text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;"><b><i>jawab:</i></b></span><br /><div class="MsoNormal"><span style="font-family: "times" , "times new roman" , serif;">Andaikan ada bilangan rasional s yang memenuhi <i>s<sup>2</sup></i>= 6. Karena <i>s</i> adalah bilangan rasional, maka kita tuliskan <i>s = p/q</i>, untuk suatu <i>p,q </i><i>€</i><i> Z</i> dimana<i> p</i> dan <i>q</i> relatif prima (atau dengan kata lain gcd(p,q) = 1). Sekarang,perhatikan bahwa s<sup>2</sup> = (p/q)<sup>2</sup> = p<sup>2</sup>/q<sup>2</sup>= 6 à p<sup>2</sup> = 6q<sup>2</sup>. Hal ini berarti p<sup>2</sup> adalah genap. Sebagai akibatnya p juga genap. Oleh sebab itu, maka kita bisa tuliskan p= 2m untuk suatu m € Z. Selanjutnya p<sup>2</sup></span><br /><a name='more'></a><span style="font-family: "times" , "times new roman" , serif;"> = (2m)<sup>2</sup> = 4m<sup>2</sup> = 6q<sup>2</sup> <--> 2m<sup>2</sup> = 3q<sup>2</sup>. Hal ini berarti 3q<sup>2</sup> adalah genap. Karena 3q<sup>2</sup> genap sedangkan 3 adalah ganjil, maka bisa kita simpulkan bahwa q<sup>2</sup> adalah genap. Dan sebagai </span>akibatnya, q juga genap. Namun, hal ini mengakibatkan q2 adalah genap. Dan sebagai akibatnya, q juga genap. Namun hal ini mengakibatkan bahwa p dan q sama-sama genap atau dengan kata lain p dan q tidak relative prima karena gcd(p,q) ≠ 1. Jadi, pengandaian bahwa ada bilangan rasional s yang memenuhi s2 = 6 adalah tidak benar. Dan haruslah tidak ada bilangan rasional s yang memenuhi s2 = 6.</div><div class="MsoNormal"><br /></div><div class="MsoNormal"><b>soal no 7</b></div><div class="MsoNormal">7). Buktikan bahwa tidak ada bilangan rasional t yang memnuhi t<sup>2</sup>= 3</div><div class="MsoNormal"><br /></div><div class="MsoNormal"><o:p></o:p></div><div class="MsoNormal"><b><i>Jawab:</i></b></div><div class="MsoNormal">Andaikan ada bilangan rasional t yang memenuhi t<sup>2</sup> = 3. Karena t adalah bilangan rasional, maka kita bisa menuliskan t = a/b untuk suatu <i>a,b</i> <i style="font-family: Times, 'Times New Roman', serif;">€ Z </i>dimana <i>a</i> dan <i>b</i> relatif prima (atau dengan kata lain gcd(a,b) = 1). Sekarang perhatikan bahwa t<sup>2</sup> = . Hal ini berarti a<sup>2</sup> habis dibagi 3. Namun hal ini mengakibatkan bahwa a juga habis dibagi 3 (mengingat jika a = 3m + 1, maka a<sup>2</sup> = (3m + 1)<sup>2</sup> = 3(3m<sup>2</sup> + 2m) + 1. Atau jika a = 3m + 2, maka a<sup>2</sup> = (3m + 2)<sup>2</sup> = 3(3m<sup>2</sup>+ 4m + 1) + 1, untuk suatu m <i style="font-family: Times, 'Times New Roman', serif;">€ Z</i> ). Selanjutnya kita bisa tuliskan a<sup>2</sup> = (3m)<sup>2 </sup>= 9m<sup>2</sup> = 3b<sup>2</sup> <--> 3m<sup>2</sup> = b<sup>2</sup>. Namun hal ini mengakibatkan b<sup>2</sup> habis dibagi 3. Dan selanjutnya, kita tahu bahwa b juga habis dibagi 3. Sehingga dapat disimpulkan bahwa a dan b sama-sama habis dibagi 3. Hal ini berkontradiksi dengan asumsi awal yang mengatakan bahwa a dan b adalah relatif prima.</div><div class="MsoNormal"><br /></div><div class="MsoNormal"><b>soal no 8</b></div><div class="MsoNormal">8). a) Tunjukkan bahwa jika x,y adalah bilangan rasional , maka x + y dan xy adalah bilangan rasional</div><div class="MsoNormal"> b) Buktikan bahwa, jika x adalah bilangan rasional dan y adalah bilangan irrasional, maka x + y adalah bilangan irrasional. Dan jika ditambahkan syarat untuk x ≠ 0, tunjukkan bahwa xy adalah bilangan irrasional.</div><div class="MsoNormal"><br /></div><div class="MsoNormal"><b><i>jawab:</i></b></div><div class="MsoNormal"> a). Misalkan x € Q, maka x = a/b, untuk suatu <i>a,b € Z</i> dan misalkan <i>y € Q</i>, maka y = c/d, untuk suatu <i>c,d € Z</i>. Selanjutnya, perhatikan bahwa: x + y = a/b + c/d = (ad + bc)/bd <i>€ Q</i> mengingat bahwa <i>ad + cb € Z </i>dan<i> b,d € Z</i>. Kemudian dengan cara yang sama kita dapat menunjukkan bahwa x,y = a/b . c/d = ac/bd <i>€ Q</i> mengingat <i>a, c € Z </i>dan<i> b,d € Z</i>.<o:p></o:p></div><div class="MsoNormal"><br /></div><div class="MsoNormal">b). Andaikan x + y € Q, maka x + y = m/n untuk suatu m,n € Z. Sekarang perhatikan bahwa: x + y = m/n <-> y = m/n – x = m/n – a/b = (mb – an)/nb. Karena <i>m b – a n </i><i>€</i><i> Z </i>dan <i>n b </i><i>€</i><i> Z</i>, maka y= (mb – an)/nb <i>€</i> <i>Q</i>yang berkontradiksi dengan hipotesis yang mengatakan y Ɇ Q. Jadi haruslah bahwa x + y Ɇ Q. Selanjutnya andaikan x,y € Q, maka xy = p/q untuk suatu p,q € Z. Sekarang perhatikan bahwa: xy = p/q . 1/x = p/q . 1/(a/b) = p/q . b/a = pb/qa. Karena <i>p b € Z</i>, dan <i>q a € Z</i> , maka y = pb/qa € Q. Jadi, haruslah x y Ɇ Q.</div><div class="MsoNormal"><br /></div><div class="MsoNormal"><b>soal no 9. </b></div><div class="MsoNormal"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtHMCYgZQEvA5oJKszfGmuL7aGxB9aGEwyb7yGXrMex6v6BMl-PUOwDRV5kMr6xGC1nk2_vuVHOqs5j5hNddlD9pOrvKqRYcc5ZOR7aBLm9Qv_hgdLLKWTNH9pbcft1tbOLpI3RSAqEbI/s1600/soal+no+9.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtHMCYgZQEvA5oJKszfGmuL7aGxB9aGEwyb7yGXrMex6v6BMl-PUOwDRV5kMr6xGC1nk2_vuVHOqs5j5hNddlD9pOrvKqRYcc5ZOR7aBLm9Qv_hgdLLKWTNH9pbcft1tbOLpI3RSAqEbI/s1600/soal+no+9.jpg" /></a></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><br /></div><div class="MsoNormal"><b><i>jawab:</i></b></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitwDyWswiVcq0tYV1KssXttwm8JtyI1U25Qbrn2kyYcj2CAXPzbU-P495O3VEzvtJhpdBfV9zpOQi_sf64dtaPALdFmbxpAgGGWIxw27ijmACOtkKIRE13vyLQVc1kfnoUH1An37n8Inw/s1600/jawaban+no+9+a.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitwDyWswiVcq0tYV1KssXttwm8JtyI1U25Qbrn2kyYcj2CAXPzbU-P495O3VEzvtJhpdBfV9zpOQi_sf64dtaPALdFmbxpAgGGWIxw27ijmACOtkKIRE13vyLQVc1kfnoUH1An37n8Inw/s1600/jawaban+no+9+a.jpg" /></a></div><div class="MsoNormal"><b><i><br /></i></b></div><div class="MsoNormal"><b><i><br /></i></b></div><div class="MsoNormal"><b><i><br /></i></b></div><div class="MsoNormal"><b><i><br /></i></b></div><div class="MsoNormal"><b><i><br /></i></b></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKof5ndF5ltDDTjWyDTF1Jl1NohS_lSLwKZE0JpypUyo7pyD6tG1OWUeSFoMUIjz2pJFPnYUcIRDSQQXP_C9CRRzBAzL-y5tcaXnanaBmRJL9ymUzUfzHvUQfmL3iJmqtFgVgPziJGRTA/s1600/jawaban+no+9b.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKof5ndF5ltDDTjWyDTF1Jl1NohS_lSLwKZE0JpypUyo7pyD6tG1OWUeSFoMUIjz2pJFPnYUcIRDSQQXP_C9CRRzBAzL-y5tcaXnanaBmRJL9ymUzUfzHvUQfmL3iJmqtFgVgPziJGRTA/s1600/jawaban+no+9b.jpg" /></a></div><div class="MsoNormal"><b><i><br /></i></b></div><div class="MsoNormal"><b><i><br /></i></b></div><div class="MsoNormal"><b><i><br /></i></b></div><div class="MsoNormal"><b><i><br /></i></b></div><div class="MsoNormal"><b><i><br /></i></b></div><div class="MsoNormal"><b><i><br /></i></b></div><div class="MsoNormal"><b><i><br /></i></b></div><div class="MsoNormal"><b><i><br /></i></b></div><div class="MsoNormal"><b>soal no 10</b></div><div class="MsoNormal"><b>10.</b></div><div class="MsoNormal"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNCWpaH5WA8nN2YlBxisW-puBMo9Rn9CJ84SuCq6nP0fd9AAQF8pZ9rv1ehY08mu0wp97aNfKWH7pw6EyEM2e_9Mrw6lKHkVKSGpYlaCmoYaNA6GVlUxfrmpRiIYsSbdFodEVYpw0wd2o/s1600/soal+no+10.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="28" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNCWpaH5WA8nN2YlBxisW-puBMo9Rn9CJ84SuCq6nP0fd9AAQF8pZ9rv1ehY08mu0wp97aNfKWH7pw6EyEM2e_9Mrw6lKHkVKSGpYlaCmoYaNA6GVlUxfrmpRiIYsSbdFodEVYpw0wd2o/s400/soal+no+10.jpg" width="400" /></a><b><br /></b></div><div class="MsoNormal"><b><br /></b></div><div class="MsoNormal" style="text-align: left;"><br /></div><div class="MsoNormal" style="text-align: justify;"><i><b>jawab:</b></i></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivWGv8Cp77UC_nBgcin_yAw5E-AFAKU60Y-QPDspCKuQQ-eRHiVgRIlkgKqeANZoFvDOUK-yYTTyLAh6g6MTh2L2n-VPEChzbMKRoGHTAcsZ6olKxxHzasLEWDZzMqTCkSSHBiDDtcV3Q/s1600/jawaban+no+10+a.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivWGv8Cp77UC_nBgcin_yAw5E-AFAKU60Y-QPDspCKuQQ-eRHiVgRIlkgKqeANZoFvDOUK-yYTTyLAh6g6MTh2L2n-VPEChzbMKRoGHTAcsZ6olKxxHzasLEWDZzMqTCkSSHBiDDtcV3Q/s1600/jawaban+no+10+a.jpg" /></a></div><div class="MsoNormal"><b><br /></b></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisHiMOg04OrHQmjv7l8kxzs3nheF4IT3_pAeByLZpth89MSfoQqh1b-65a9yZzNfBgF25JHjan977SMdoIOkbQAdlK4UGvhgDFzC2OYXNKDDpoKB7hrC6VVGUgiuhbmuIVFZ2wH4CpnaY/s1600/jawaban+no+10+b1.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisHiMOg04OrHQmjv7l8kxzs3nheF4IT3_pAeByLZpth89MSfoQqh1b-65a9yZzNfBgF25JHjan977SMdoIOkbQAdlK4UGvhgDFzC2OYXNKDDpoKB7hrC6VVGUgiuhbmuIVFZ2wH4CpnaY/s1600/jawaban+no+10+b1.jpg" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgd4gqPF-NIcgA2UdzoX6S3nr8rgSahSNYrs7vdoafR_9tEq65Uaii4IS4NbTglb5jJ9zMLPPAsE6w5ALOSN9YC5C1Jcowjmj-sWEQxFRiApQeRyEfwqur4spOsA1vWLXqZo0o0kT5K9u8/s1600/jawaban+no+10b2.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgd4gqPF-NIcgA2UdzoX6S3nr8rgSahSNYrs7vdoafR_9tEq65Uaii4IS4NbTglb5jJ9zMLPPAsE6w5ALOSN9YC5C1Jcowjmj-sWEQxFRiApQeRyEfwqur4spOsA1vWLXqZo0o0kT5K9u8/s1600/jawaban+no+10b2.jpg" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">Setelah menyimak pembahasan analisis real 2.1 apakah kalian mengalami kesulitan? pasti tidak kan :). Nah untuk menambah pengetahuan dan kemampuan mengerjakan soal tentang analisis real, silahkan baca juga<b><span style="color: blue;"> <a href="http://funmathscience.blogspot.co.id/2015/12/lanjutan-jawaban-soal-analisis-real-1.html" target="_blank">lanjutan pembahasan soal analisis real 1. latihan 2.1 soal np 11-20</a></span></b></div><div class="MsoNormal"><b><br /></b></div><div class="MsoNormal"><b></b></div><div class="MsoNormal"><o:p></o:p></div><div class="MsoNormal"><o:p></o:p></div><div class="MsoNormal"><o:p></o:p></div><div class="MsoNormal"><o:p></o:p></div></div></div></div> Untuk membantu anda keluar dari jerat kesulitan mengerjakan soal analisis real 1, saya akan membantu dengan postingan soal analisi real 1 ya... Read more »
Basis dan Dimensi November 29, 2015 Basis , bebas , bergantung , dimensi , Kombinasi , linier , matriks , Ruang , subruang , Vektor <div dir="ltr" style="text-align: left;" trbidi="on"><div class="MsoNormal" style="line-height: 200%; text-align: justify; text-indent: 36.0pt;"><span style="font-size: large;">Pengertian basis untuk ruang vektor V serupa dengan pengertian basis untuk R<sup>n</sup>, yang telah kita kenal. Untuk mengenal basis, diperlukan pengertian membangun dan bebas linier. Pengertian membangun telah kita pelajari di materi sebelumnya yaitu <a href="http://funmathscience.blogspot.co.id/2015/08/kombinasi-linear-bebas-linear.html" target="_blank">kombinasi,bergantung, dan bebas linier</a> . Dengan pengertian bebas linier, himpunan yang membangun V dapat diperkecil sedemikian mungkin sehingga himpunan yang baru tetap membangun V.</span></div><br /><div class="MsoNormal" style="line-height: 200%; text-align: justify;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBXM_EBU-DcWAeSW_TD7x_B8OYwbRLzSDiZy5c-qFhVHmTPgyrIFLVeEtbfREWUX2FJPVRNAiTO7U5Cm5DTOW1NlBbjlt-Bs1XQ_zimlK27bQlBq2VRx9EWiwRJa1cxq836mNcWYJqwVc/s1600/basis.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: left;"><img border="0" height="65" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBXM_EBU-DcWAeSW_TD7x_B8OYwbRLzSDiZy5c-qFhVHmTPgyrIFLVeEtbfREWUX2FJPVRNAiTO7U5Cm5DTOW1NlBbjlt-Bs1XQ_zimlK27bQlBq2VRx9EWiwRJa1cxq836mNcWYJqwVc/s400/basis.jpg" width="400" /></a></div><span style="font-size: large;"><i><br /></i></span><span style="font-size: large;"><i><br /></i></span><span style="font-size: large;"><i></i></span><br /><a name='more'></a><span style="font-size: large;"><i><br /></i></span><span style="font-size: large;"><i>Definisi</i></span></div><div class="MsoNormal" style="line-height: 200%; text-align: justify;"><span style="font-size: large;">Contoh :</span></div><div class="MsoNormal" style="line-height: 200%; text-align: justify;"><span style="font-size: large;">Misalkan p(x) = 2 – 3x + x<sup>2</sup> , q(x) = 1 + x – x<sup>2</sup> , r(x) = 5 – 5x + x<sup>2</sup>untuk setiap x real. Karena 2p + g – r = 0 maka {p, q, r} bergantung linier di P<sub>2</sub></span></div><div class="MsoNormal" style="line-height: 200%; text-align: justify;"></div><div class="MsoNormal" style="line-height: 200%; text-align: justify;"><span style="font-size: large;"><u>Sifat</u> :</span></div><div class="separator" style="clear: both; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnfVG04GO3r9oV6lhRfQ_z4Z513xKcCMPKEtYUbp0ZDRoxBKtSkR-M70bWsxGnt_TwHfydBjsqmTAijJv0Yaoipr9PbNl-INe4qcAnGuCrw0aLUI9-kk9R3SUasEyw3sjCWBTJvDKUYZw/s1600/basis+2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: large;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnfVG04GO3r9oV6lhRfQ_z4Z513xKcCMPKEtYUbp0ZDRoxBKtSkR-M70bWsxGnt_TwHfydBjsqmTAijJv0Yaoipr9PbNl-INe4qcAnGuCrw0aLUI9-kk9R3SUasEyw3sjCWBTJvDKUYZw/s400/basis+2.jpg" width="400" /></span></a></div><div class="separator" style="clear: both; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimrtNrITsOSsT_bFVJO2M7LHWLAl7eg8f_Bbnrck-N0dAC0rEGey6AcXd6lGtUrkjbHxeYLrKoZDl3xlsSKCOHwMHFIeH-n_61SKSjk_oz0turgWHtoffWE03ecH1XWZ4r2RejMs5mY7k/s1600/basis+3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: large;"><img border="0" height="172" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimrtNrITsOSsT_bFVJO2M7LHWLAl7eg8f_Bbnrck-N0dAC0rEGey6AcXd6lGtUrkjbHxeYLrKoZDl3xlsSKCOHwMHFIeH-n_61SKSjk_oz0turgWHtoffWE03ecH1XWZ4r2RejMs5mY7k/s400/basis+3.jpg" width="400" /></span></a></div><div class="separator" style="clear: both; text-align: justify;"><span style="font-size: large;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1ZrQhFOqnEYwlp6tnnxL5hodx1rNWo5OcAygGv4Bi3nwzPaVm5Pq6OWVhDQtEbL4hYplE0-fRWl57ceUYlChHZm6F_kg2CVKTdaVJn0q-DicNhxLW1icRHwUZEz1ybH67dOpIJ80AG1M/s1600/basis+5.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5hhfkbs6rpnVUqKF1ZldeV3iH-vwbIcbpvQ6fd3TaVDmdMjUjAZvONrgbJSDubTpVFt7rknLYM_9L5ScjfMID_tB3bQmJwQL-x8AdbpkjpcRnv7HfrtxRseSEqlIUwgutYiRKWthiNt4/s1600/basis+4.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em; text-align: justify;"><span style="font-size: large;"><img border="0" height="160" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5hhfkbs6rpnVUqKF1ZldeV3iH-vwbIcbpvQ6fd3TaVDmdMjUjAZvONrgbJSDubTpVFt7rknLYM_9L5ScjfMID_tB3bQmJwQL-x8AdbpkjpcRnv7HfrtxRseSEqlIUwgutYiRKWthiNt4/s400/basis+4.jpg" width="400" /></span></a></div><div style="text-align: justify;"><span style="font-size: large;"><img border="0" height="148" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1ZrQhFOqnEYwlp6tnnxL5hodx1rNWo5OcAygGv4Bi3nwzPaVm5Pq6OWVhDQtEbL4hYplE0-fRWl57ceUYlChHZm6F_kg2CVKTdaVJn0q-DicNhxLW1icRHwUZEz1ybH67dOpIJ80AG1M/s400/basis+5.jpg" width="400" /></span></div><br /><div style="text-align: justify;"><span style="font-size: large;"> <i>Definisi :</i></span></div><div class="MsoNormal" style="line-height: 200%; text-align: justify;"><i><span style="font-size: large;">Ruang vektor tak nol V dikatakan berdimensi hingga, jika V mempunyai basis yang hingga. Banyaknya vektor dalam suatu basis untuk V disebut dimensi (V), disingkat dim(V). dimensi ruang vektor nol didefinisikan nol.</span></i></div><div class="MsoNormal" style="line-height: 200%; text-align: justify;"><span style="font-size: large;">Contoh :</span></div><div class="MsoNormal" style="line-height: 200%; text-align: justify;"></div><ol start="1" style="margin-top: 0mm;" type="1"><li class="MsoNormal" style="line-height: 200%; mso-list: l0 level1 lfo1; tab-stops: list 36.0pt; text-align: justify;"><span style="font-size: large;">Dimensi (<span style="font-family: "symbol"; mso-ascii-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;">Â</span><sup>n</sup>) = n sebab memiliki basis yang terdiri dari n vektor.</span></li><li class="MsoNormal" style="line-height: 200%; mso-list: l0 level1 lfo1; tab-stops: list 36.0pt; text-align: justify;"><span style="font-size: large;">Dimensi (P<sub>n</sub>) = n + 1 sebab memiliki basis yang terdiri dari n + 1 vektor</span></li><li class="MsoNormal" style="line-height: 200%; mso-list: l0 level1 lfo1; tab-stops: list 36.0pt; text-align: justify;"><span style="font-size: large;">Jika M<sub>2</sub> ruang vektor yang terdiri dari matriks 2x2 dengan komponen real maka dimensi (M<sub>2</sub>) = 4, sebab M<sub>2</sub> mempunyai basis yang terdiri dari 4 unsur.</span></li></ol><span style="font-size: large;"><u style="line-height: 200%; text-align: justify;">Sifat</u><span style="line-height: 200%; text-align: justify;"> :</span><br /><span style="line-height: 200%; text-align: justify;"> Jika V ruang vektor berdimensi n, maka :</span></span><br /><ol start="1" style="line-height: 200%; margin-top: 0mm; text-align: justify;" type="1"><li class="MsoNormal" style="line-height: 200%; mso-list: l0 level1 lfo1; tab-stops: list 36.0pt; text-align: justify;"><span style="font-size: large;">Setiap himpunan m vektor di V dengan m > n, senantiasa bergantung linier</span></li><li class="MsoNormal" style="line-height: 200%; mso-list: l0 level1 lfo1; tab-stops: list 36.0pt; text-align: justify;"><span style="font-size: large;">Setiap himpunan n vektor di V yang bebas linier, membentuk basis untuk V</span></li><li class="MsoNormal" style="line-height: 200%; mso-list: l0 level1 lfo1; tab-stops: list 36.0pt; text-align: justify;"><span style="font-size: large;">Setiap himpunan n vektor di V yang membangun V, membentuk basis untuk V</span></li><li class="MsoNormal" style="line-height: 200%; mso-list: l0 level1 lfo1; tab-stops: list 36.0pt; text-align: justify;"><span style="font-size: large;">Setiap himpunan k vektor yang bebas linier di V, dengan k < n dapat diperluas menjadi suatu basis untuk V</span></li></ol><h4 style="text-align: justify;"><span style="font-size: large;">Soal Latihan </span></h4><div class="MsoNormal" style="line-height: 200%; margin-left: 18.7pt; mso-list: l0 level1 lfo1; text-align: justify; text-indent: -18.7pt;"><!--[if !supportLists]--><span style="font-size: large;">1.<span style="font-stretch: normal; line-height: normal;"> </span><!--[endif]-->Diketahui <!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1510391454"> </o:OLEObject></xml><![endif]--></span></div><div class="separator" style="clear: both; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUlRZ0c36-SyCzjLjrdIlMpBZ4N-xPqcWjoxftV9y0Fm0db6zpgLkGEXxk_Pq4XS8cI7SmxkUp39Gajj_qG08ZYe8miujYrevLXEr2j8vXfJQ4a3QKsWvXybfcR3RUPMfe58xMOrUsjdk/s1600/matrixs+basis.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: large;"><img border="0" height="93" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUlRZ0c36-SyCzjLjrdIlMpBZ4N-xPqcWjoxftV9y0Fm0db6zpgLkGEXxk_Pq4XS8cI7SmxkUp39Gajj_qG08ZYe8miujYrevLXEr2j8vXfJQ4a3QKsWvXybfcR3RUPMfe58xMOrUsjdk/s200/matrixs+basis.jpg" width="200" /></span></a></div><span style="mso-text-raise: -27.0pt; position: relative; top: 27.0pt;"><span style="font-size: large;"><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"/> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"/> <v:f eqn="sum @0 1 0"/> <v:f eqn="sum 0 0 @1"/> <v:f eqn="prod @2 1 2"/> <v:f eqn="prod @3 21600 pixelWidth"/> <v:f eqn="prod @3 21600 pixelHeight"/> <v:f eqn="sum @0 0 1"/> <v:f eqn="prod @6 1 2"/> <v:f eqn="prod @7 21600 pixelWidth"/> <v:f eqn="sum @8 21600 0"/> <v:f eqn="prod @7 21600 pixelHeight"/> <v:f eqn="sum @10 21600 0"/> </v:formulas> <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/> <o:lock v:ext="edit" aspectratio="t"/></v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style='width:168.75pt; height:60pt' o:ole=""> <v:imagedata src="file:///C:\Users\Pramono\AppData\Local\Temp\msohtmlclip1\01\clip_image001.wmz" o:title=""/></v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span></span><br /><div class="MsoNormal" style="line-height: 200%; text-align: justify;"><span style="font-size: large;"> Tunjukkan K ruang bagian dari R<sup>3</sup>. Kemudian tentukan suatu basis untuk K</span></div><div class="MsoNormal" style="line-height: 200%; margin-left: 18.7pt; mso-list: l0 level1 lfo1; text-align: justify; text-indent: -18.7pt;"><!--[if !supportLists]--><span style="font-size: large;">2.<span style="font-stretch: normal; line-height: normal;"> </span>Tentukan suatu basis dan dimensi ruang vektor M<sub>mxn</sub></span></div><div class="MsoNormal" style="line-height: 200%; margin-left: 18.7pt; mso-list: l0 level1 lfo1; text-align: justify; text-indent: -18.7pt;"><!--[if !supportLists]--><span style="font-size: large;">3.<span style="font-stretch: normal; line-height: normal;"> </span>Tentukan suatu basis dan dimensi ruang bagian dari P<sub>n</sub>, berikut :</span></div><div class="MsoNormal" style="line-height: 200%; text-align: justify; text-indent: 18.7pt;"><span style="font-size: large;">a. {p <span style="font-family: "symbol"; mso-ascii-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;">ÃŽ</span> P<sub>n</sub> | p (1) = 0} b. {p <span style="font-family: "symbol"; mso-ascii-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;">ÃŽ</span> P<sub>n</sub> | p’(1) = 0</span>}</div></div> Pengertian basis untuk ruang vektor V serupa dengan pengertian basis untuk R n , yang telah kita kenal. Untuk mengenal basis, diperlukan pen... Read more »
Jawaban soal Kombinasi Linier, Bergantung Linier, dan Bebas Linier November 29, 2015 bebas , bergantung , homogen , jawaban , Kombinasi , linier , persamaan , polinomial , Soal , SPL , Vektor <div dir="ltr" style="text-align: left;" trbidi="on"><div style="text-align: justify;">Setelah kita pahami materi tentang kombinasi linier, bergantung linier dan bebas linier. sudah saatnya kita membahas jawaban dari soal di latihan pada artikel <b style="color: blue;"><a href="http://funmathscience.blogspot.co.id/2015/08/kombinasi-linear-bebas-linear.html">kombinasi linier, bergantung linier, dan bebas linier</a>. </b>Mari kita cermati pembahasan soalnya di bawah ini:</div><div style="text-align: justify;"><br /><a name='more'></a><br /></div><div style="text-align: justify;">1). <span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px; text-align: justify; text-indent: -17.95pt;">Misal u = (2, 4, 0), dan v = (1, –1, 3) adalah vektor-vektor di R</span><sup style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 18.48px; text-align: justify; text-indent: -17.95pt;">3</sup><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px; text-align: justify; text-indent: -17.95pt;">.</span></div><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px; text-align: justify; text-indent: -17.95pt;"> </span><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px; text-align: justify; text-indent: -17.95pt;">Apakah vektor berikut merupakan kombinasi linear dari vektor – vektor di atas</span><br /><span style="color: #222222; font-family: "times new roman" , serif; font-size: 10pt; line-height: 18.48px; text-align: justify; text-indent: -17.95pt;"> a.<span style="font-family: "times new roman"; font-size: 7pt; font-stretch: normal;"> </span></span><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px; text-align: justify; text-indent: -17.95pt;">h = (4, 2, 6)</span><br /><span style="color: #222222; font-family: "times new roman" , serif; font-size: 10pt; line-height: 18.48px; text-align: justify; text-indent: -17.95pt;"> b.<span style="font-family: "times new roman"; font-size: 7pt; font-stretch: normal;"> </span></span><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px; text-align: justify; text-indent: -17.95pt;">j = (1, 5, 6)</span><br /><span style="color: #222222; font-family: "times new roman" , serif; font-size: 10pt; line-height: 18.48px; text-align: justify; text-indent: -17.95pt;"> c.<span style="font-family: "times new roman"; font-size: 7pt; font-stretch: normal;"> </span></span><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px; text-align: justify; text-indent: -17.95pt;">r = (0, 0, 0)</span><br /><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px; text-align: justify; text-indent: -17.95pt;"><b>Jawab:</b></span><br /><div class="separator" style="clear: both; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhM-cbck8APut8u8iYdjLTG2tyN37pJ-RIFRTFm2eitx2ieB8Zkfu20Zp_YsvaZ_quZqgjHbCsmZfsaR-onkMkaUjPA-yOvnY6iS2hbBr30J6TrV7fkWcW3UKxboR8ndpy-Je7PyoGVkLQ/s1600/jawaban+no+1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="jawaban kombinasi linier" border="0" height="87" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhM-cbck8APut8u8iYdjLTG2tyN37pJ-RIFRTFm2eitx2ieB8Zkfu20Zp_YsvaZ_quZqgjHbCsmZfsaR-onkMkaUjPA-yOvnY6iS2hbBr30J6TrV7fkWcW3UKxboR8ndpy-Je7PyoGVkLQ/s320/jawaban+no+1.jpg" title="jawaban no 1 kombinasi linier" width="320" /></a></div><div class="separator" style="clear: both; text-align: justify;"> ini juga dapat ditulis menjadi</div><div class="separator" style="clear: both; text-align: justify;"> </div><div class="separator" style="clear: both; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2SWfnq-iYS-4okeBl-sRvSb3ckgGl7DwcvkVfg4Hfr_rD5I22diSeCL7KgA0QaAgthvpFgA7UKCjEo4EuPLxVCJz7ltuFIRMrmRv-KMD6eikRPU2w8774EgUfQ0fIvGYJDGwvAsRKS4c/s1600/lanjutan+jawaban+no+1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="lanjutan soal kombinasi no 1" border="0" height="166" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2SWfnq-iYS-4okeBl-sRvSb3ckgGl7DwcvkVfg4Hfr_rD5I22diSeCL7KgA0QaAgthvpFgA7UKCjEo4EuPLxVCJz7ltuFIRMrmRv-KMD6eikRPU2w8774EgUfQ0fIvGYJDGwvAsRKS4c/s320/lanjutan+jawaban+no+1.jpg" title="lanjutan soal no 1" width="320" /></a></div><div class="separator" style="clear: both; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_2L9dz1OHTYYy2DHO8p5k5WOhF_ep3PmYKg_leFXMLE9TqrxB8ff71YcIvbyI9Io0Zay8huIscQtcS2iFDQrlYvZHjjzeRlIv8yNpSBVdkArxDkHISkzrrgwdJJIJQ20sbW3YyG_IHic/s1600/jawaban+no+1b.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="jawaban kombinasi linier no 1b" border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_2L9dz1OHTYYy2DHO8p5k5WOhF_ep3PmYKg_leFXMLE9TqrxB8ff71YcIvbyI9Io0Zay8huIscQtcS2iFDQrlYvZHjjzeRlIv8yNpSBVdkArxDkHISkzrrgwdJJIJQ20sbW3YyG_IHic/s320/jawaban+no+1b.jpg" title="jawaban no 1b" width="317" /></a></div><div class="separator" style="clear: both; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3pscGSAP8HcTuPjLma6Kv4S8A4vLzWgrShfKhRYihAe-IftAxwkTgkz02DKxiOA_4XqeD-xnCemiC0CfsFHkAjG4Ievj_51IPfgxDHHPVF0wBJORk4BmUYBhKgH6ZjQD0UGxcpxuT4hY/s1600/jawaban+no+1c.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="jawaban kombinasi linier 1c" border="0" height="29" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3pscGSAP8HcTuPjLma6Kv4S8A4vLzWgrShfKhRYihAe-IftAxwkTgkz02DKxiOA_4XqeD-xnCemiC0CfsFHkAjG4Ievj_51IPfgxDHHPVF0wBJORk4BmUYBhKgH6ZjQD0UGxcpxuT4hY/s320/jawaban+no+1c.jpg" title="jawaban no 1c" width="320" /></a></div><div class="separator" style="clear: both; text-align: justify;"> </div><div class="separator" style="clear: both; text-align: justify;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9Mv6OWk-XkQTG6iSf6OD2aHL-dNhyX_a2wQWmpjGtfpqumfCK0H5JDARHl6yN1adfkWUxSl1XnLjvlE9sUk8_KlCXL1FrQNNQ2VUGhyphenhyphenYj6D-6DL0aEH_ir_b8MFyQGYGI7GUjGYvf_8Y/s1600/jawaban+lanjutan+no+1c.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="lanjutan jawaban kombinasi linier no 1c" border="0" height="64" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9Mv6OWk-XkQTG6iSf6OD2aHL-dNhyX_a2wQWmpjGtfpqumfCK0H5JDARHl6yN1adfkWUxSl1XnLjvlE9sUk8_KlCXL1FrQNNQ2VUGhyphenhyphenYj6D-6DL0aEH_ir_b8MFyQGYGI7GUjGYvf_8Y/s320/jawaban+lanjutan+no+1c.jpg" title="lanjutan jawaban no 1c" width="320" /></a></div><div class="separator" style="clear: both; text-align: justify;"><br /></div><div class="separator" style="clear: both; text-align: justify;">2). <span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px; text-align: justify; text-indent: -23.9333px;">Diketahui v =(3,9,-4,-2) merupakan kombinasi linier u</span><sub style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; text-align: justify; text-indent: -23.9333px;">1</sub><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px; text-align: justify; text-indent: -23.9333px;">= (1,-2,0,3), u</span><sub style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; text-align: justify; text-indent: -23.9333px;">2</sub><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px; text-align: justify; text-indent: -23.9333px;"> = (2,3,0,-1) dan u</span><sub style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; text-align: justify; text-indent: -23.9333px;">3</sub><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px; text-align: justify; text-indent: -23.9333px;">= (2,-1,2,1). Apakah v merupakan kombinasi linear dari u</span><sub style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; text-align: justify; text-indent: -23.9333px;">1</sub><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px; text-align: justify; text-indent: -23.9333px;"> , u</span><sub style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; text-align: justify; text-indent: -23.9333px;">2</sub><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px; text-align: justify; text-indent: -23.9333px;">dan u</span><sub style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; text-align: justify; text-indent: -23.9333px;">3</sub><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px; text-align: justify; text-indent: -23.9333px;"> ?</span></div><div class="separator" style="clear: both; text-align: justify;"><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px; text-align: justify; text-indent: -23.9333px;">Jawab: </span></div><div class="separator" style="clear: both; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhArz7JngehKmUHWlNCBuYM_eI_XH2CdDyrNLAvfOZfyW3LQ2-2iTMzUTFzU1NlR0FBQ9zPBDvamW4BupKdxsrdL0PbRj8AN_Wa9rGgbELyhNXXXPk1jAfw-WR3YkhbSJFkk0vzwyXHxMo/s1600/jawaban+no+2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: left;"><img border="0" height="123" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhArz7JngehKmUHWlNCBuYM_eI_XH2CdDyrNLAvfOZfyW3LQ2-2iTMzUTFzU1NlR0FBQ9zPBDvamW4BupKdxsrdL0PbRj8AN_Wa9rGgbELyhNXXXPk1jAfw-WR3YkhbSJFkk0vzwyXHxMo/s320/jawaban+no+2.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjybHakYboB_h0i-wPqVGrNArDHHUAF0O_15bFiM2qJ3M1dXY4NUaq_uWVlNbVIHFGRQMP1C1vx9sjC539G9RegiUcKG-2HPnghZhkfQ83dUuc29G7o2Zz2yIj2gknoinCnBp0Hwtu9uk/s1600/lanjutan+jawaban+no+2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="162" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjybHakYboB_h0i-wPqVGrNArDHHUAF0O_15bFiM2qJ3M1dXY4NUaq_uWVlNbVIHFGRQMP1C1vx9sjC539G9RegiUcKG-2HPnghZhkfQ83dUuc29G7o2Zz2yIj2gknoinCnBp0Hwtu9uk/s320/lanjutan+jawaban+no+2.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: justify;"> Penyelesaiannya: x = 1, y = 3, dan z = -2</div><div class="separator" style="clear: both; text-align: justify;"><br /></div><div class="separator" style="clear: both; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGaKsGyCaIyUl0PZuYEH8ji4q6y3U46lApqGkjKWLBJ1idGerwARAXe1c7UCLK__sg5p3EtKYltfzSsvF5Pe4IdnXiT2kVv6oIwSOdpYCZ8IrWLcYO1M_nvzA1vLoQOmwImFCs8XYFLH0/s1600/lanjutan+soal+no+2.1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="88" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGaKsGyCaIyUl0PZuYEH8ji4q6y3U46lApqGkjKWLBJ1idGerwARAXe1c7UCLK__sg5p3EtKYltfzSsvF5Pe4IdnXiT2kVv6oIwSOdpYCZ8IrWLcYO1M_nvzA1vLoQOmwImFCs8XYFLH0/s200/lanjutan+soal+no+2.1.jpg" width="200" /></a></div><div class="separator" style="clear: both; text-align: justify;"><br /></div><div class="separator" style="clear: both; text-align: justify;">3). <span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px; text-indent: -23.9333px;">Apakah polinomial-polinomial berikut ini bebas linier ? </span></div><div class="separator" style="clear: both; text-align: justify;"><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px; text-indent: -23.9333px;"><b>p</b></span><sub style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; text-indent: -23.9333px;"><b>1</b></sub><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px; text-indent: -23.9333px;"> = 1 – 2x + 3 x</span><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; text-indent: -23.9333px;">2</sup><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px; text-indent: -23.9333px;"> , </span></div><div class="separator" style="clear: both; text-align: justify;"><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px; text-indent: -23.9333px;"><b>p</b></span><sub style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; text-indent: -23.9333px;"><b>2</b></sub><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px; text-indent: -23.9333px;"> = 5 + 6x – x</span><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; text-indent: -23.9333px;">2</sup><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px; text-indent: -23.9333px;"> , </span></div><div class="separator" style="clear: both; text-align: justify;"><b><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px; text-indent: -23.9333px;">p</span><sub style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; text-indent: -23.9333px;">3</sub></b><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px; text-indent: -23.9333px;"> = 3 + 2x + x</span><sup style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; text-indent: -23.9333px;">2</sup></div><div class="separator" style="clear: both; text-align: justify;"><br /></div><div class="separator" style="clear: both; text-align: justify;"><b>Jawab:</b></div><div class="separator" style="clear: both; text-align: justify;"><br /></div><div class="separator" style="clear: both; text-align: justify;">Untuk menguji polinomial bebas atau bergantung linier, langkah yang dilakukan adalah dengan menuliskan persamaan homogen sebagai berikut:</div><div class="separator" style="clear: both; text-align: justify;"><br /></div><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4idUk3KPKwyVIYO1HyP9Bs8hsKyU701VTo51kdV4AKrCBZk71FVd-KcHAaVNFz84tl8rwTZV8QBeuYDH0AQ45xynqtKspR257Ef_2S1pwXdiykGHf-_huleZl_ApJQT7lXwYv5p5RTLw/s1600/jawaban+no+3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="83" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4idUk3KPKwyVIYO1HyP9Bs8hsKyU701VTo51kdV4AKrCBZk71FVd-KcHAaVNFz84tl8rwTZV8QBeuYDH0AQ45xynqtKspR257Ef_2S1pwXdiykGHf-_huleZl_ApJQT7lXwYv5p5RTLw/s320/jawaban+no+3.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgA7MTFp2jX0Uly4BIoVRrss5Azl6_dDbbkG283AgZWZlbmPBRN5kC2EJ9Sx_DxedDQeQNA5TgBuzVoyz9mSQk0RSvlBH0-LVqp8BY5AHoCW6Osz2Shn2v3wHngC9CwHvd4BvqiqDEY0pM/s1600/jawaban+no+3.2.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="167" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgA7MTFp2jX0Uly4BIoVRrss5Azl6_dDbbkG283AgZWZlbmPBRN5kC2EJ9Sx_DxedDQeQNA5TgBuzVoyz9mSQk0RSvlBH0-LVqp8BY5AHoCW6Osz2Shn2v3wHngC9CwHvd4BvqiqDEY0pM/s320/jawaban+no+3.2.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">4.) <span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px; text-align: justify; text-indent: -17.95pt;">Diketahui u=(1,2), v=(2,2), w=(1,3). Tentukan: </span></div><div class="normal" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 18.48px; margin-left: 42.55pt; text-align: justify;"> a. Apakah u, v dan w membangun R<sup>2</sup>?</div><br style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 18.48px;" /><div class="normal" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 18.48px; margin-left: 42.55pt; text-align: justify;">b. Apakah u, v dan w bebas linier ?</div><div class="normal" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 18.48px; margin-left: 42.55pt; text-align: justify;"><b><i><u>(masih dalam penyelesaian)</u></i></b></div><div class="normal" style="background-color: white; color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13.2px; line-height: 18.48px; margin-left: 42.55pt; text-align: justify;"><br /></div><div class="separator" style="clear: both; text-align: left;">5). <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5zbKEWd-0TNvYVDwnQX83VMe3EBo5ywLNisb5oo2nVIzOscOCiVOBxBwyet27Bn5X-fBTjDrD7ZVHs8tsKyZuTBUU5gLSQjUz3lK3eVa95sariLW_IM2v8kk7dyRIPLEXL-a7dUj7ve4/s1600/soal+no+4.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" height="57" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5zbKEWd-0TNvYVDwnQX83VMe3EBo5ywLNisb5oo2nVIzOscOCiVOBxBwyet27Bn5X-fBTjDrD7ZVHs8tsKyZuTBUU5gLSQjUz3lK3eVa95sariLW_IM2v8kk7dyRIPLEXL-a7dUj7ve4/s640/soal+no+4.jpg" width="640" /></a></div><div class="separator" style="clear: both; text-align: left;"><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px; text-align: justify;"><b><br /></b></span></div><div class="separator" style="clear: both; text-align: left;"><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px; text-align: justify;"><b>jawab:</b></span></div><div class="separator" style="clear: both; text-align: left;"><span style="background-color: white; color: #222222; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13.2px; line-height: 18.48px; text-align: justify;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4MNogWe5e4lLIrePi4Vq51qAWcqsAx72OMjh9UxpvXL3252yE_ecxxQIifUA_UmKA8HPK3WRAPfrZEHGdB1BDiQ7DbzQ2Ai8TiLfgcBFuMetcIySlhS5i-rASbuHXkoMorHhE2-pN3LE/s1600/jawaban+no+4.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="195" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4MNogWe5e4lLIrePi4Vq51qAWcqsAx72OMjh9UxpvXL3252yE_ecxxQIifUA_UmKA8HPK3WRAPfrZEHGdB1BDiQ7DbzQ2Ai8TiLfgcBFuMetcIySlhS5i-rASbuHXkoMorHhE2-pN3LE/s640/jawaban+no+4.jpg" width="640" /></a></div><div class="MsoNormal" style="line-height: 150%; text-align: justify; text-justify: inter-ideograph;"><span lang="IN">Penyamaan komponen-komponen yang bersesuaian memberikan:</span></div><div class="MsoNormal" style="line-height: 150%; text-align: justify; text-justify: inter-ideograph;"><i><span lang="IN">x</span></i><span lang="IN"> – 2<i>y</i> = 6</span></div><div class="MsoNormal" style="line-height: 150%; text-align: justify; text-justify: inter-ideograph;"><span lang="IN">2<i>x</i> + <i>y</i> = 2.</span></div><div class="MsoNormal" style="line-height: 150%; text-align: justify; text-justify: inter-ideograph;"><span lang="IN"></span></div><div class="MsoNormal" style="line-height: 150%; text-align: justify; text-justify: inter-ideograph;"><span lang="IN">Bentuk ini adalah sistem persamaan linier yang terdiri dari dua persamaan dan dua bilangan yang tidak diketahui. Untuk memecahkan sistem persamaan linier ini dapat digunakan eliminasi Gauss-Jordan pada matriks yang dipernesarnya, yaitu:</span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiWqSqvrW33Sez8YUWLFD0hLanX5xydKqjyEcBOF-Rb21AZ9kRkv2f4ESMFqbistDG_Es3T3ROLzD3rruVtHLZO8j1HBl1a-cVSdvvqHFLPrlpxB9nEL62JID1TSstSOoO_s-0XBuyiBk/s1600/jawaban+no+4.2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" height="136" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiWqSqvrW33Sez8YUWLFD0hLanX5xydKqjyEcBOF-Rb21AZ9kRkv2f4ESMFqbistDG_Es3T3ROLzD3rruVtHLZO8j1HBl1a-cVSdvvqHFLPrlpxB9nEL62JID1TSstSOoO_s-0XBuyiBk/s640/jawaban+no+4.2.jpg" width="640" /></a></div><div class="MsoNormal" style="line-height: 150%; text-align: justify; text-justify: inter-ideograph;"><span lang="IN"><br /></span></div><div class="MsoNormal" style="line-height: 150%; text-align: justify; text-justify: inter-ideograph;"><span lang="IN">Setelah mencermati Jawaban Latihan Soal Kombinasi Linier, Bergantung Linier, dan Bebas Linier. pasti kalian sudah bisa memahami lebih jauh tentang bab vektor. Terima kasih telah mengunjungi blog ini, semoga bermanfaat. </span></div><div class="separator" style="clear: both; text-align: justify;"><br /></div><div class="separator" style="clear: both; text-align: justify;"><br /></div></div> Setelah kita pahami materi tentang kombinasi linier, bergantung linier dan bebas linier. sudah saatnya kita membahas jawaban dari soal di la... Read more »