{"id":2613,"date":"2020-10-30T12:37:55","date_gmt":"2020-10-30T12:37:55","guid":{"rendered":"http:\/\/onlineclassesguru.com\/?p=2613"},"modified":"2020-10-30T12:37:55","modified_gmt":"2020-10-30T12:37:55","slug":"matrices","status":"publish","type":"post","link":"https:\/\/onlineclassesguru.com\/index.php\/2020\/10\/30\/matrices\/","title":{"rendered":"Matrices"},"content":{"rendered":"<style type=\"text\/css\"><\/style><p>Consider the system of equations Ax = b where the coecient matrix A has the following<br \/>\nform. We used this example in class while trying to learn the row reduction algorithm.<br \/>\nA =<br \/>\n2<br \/>\n6<br \/>\n6<br \/>\n6<br \/>\n6<br \/>\n4<br \/>\n123<br \/>\n456<br \/>\n789<br \/>\n3<br \/>\n7<br \/>\n7<br \/>\n7<br \/>\n7<br \/>\n5<br \/>\n1. Compute the null space of the matrix A. Carefully write which variables are the pivot<br \/>\nvariables and which are the free variables. Remember the pivot variables are the ones<br \/>\nfor which there is a pivot in the corresponding column. For example if there is a pivot<br \/>\nin the first two columns then x1 and x2 are pivot variables. The free variable should<br \/>\nnot have a pivot in its column.<br \/>\n2. Now let us consider a particular right hand side. The b vector of constants are given<br \/>\nas follows<br \/>\nb =<br \/>\n2<br \/>\n6<br \/>\n6<br \/>\n6<br \/>\n6<br \/>\n4<br \/>\n3<br \/>\n3<br \/>\n3<br \/>\n3<br \/>\n7<br \/>\n7<br \/>\n7<br \/>\n7<br \/>\n5<br \/>\nFind a particular solution to this system of equations xp = (x1, x2, x3).<br \/>\n3. Using the null space above write the general solutions for this system of equations.<br \/>\nWe learned in class that the general solution will have the form<br \/>\nx = xp + y<br \/>\nwhere y 2 N(A). You will notice that it has a very interesting expression. Suppose it<br \/>\nhas the form (I am not giving you the answer, this is a pseudo example)<br \/>\ny =<br \/>\n2<br \/>\n6<br \/>\n6<br \/>\n6<br \/>\n6<br \/>\n4<br \/>\nc<br \/>\nc<br \/>\nc<br \/>\n3<br \/>\n7<br \/>\n7<br \/>\n7<br \/>\n7<br \/>\n5<br \/>\nand the particular solution is xp = (x\u21e4<br \/>\n1, x\u21e4<br \/>\n2, x\u21e4<br \/>\n3). Then the general solution is<br \/>\nx =<br \/>\n2<br \/>\n6<br \/>\n6<br \/>\n6<br \/>\n6<br \/>\n4<br \/>\nc + x\u21e4<br \/>\n1<br \/>\nc + x\u21e4<br \/>\n2<br \/>\nc + x\u21e4<br \/>\n3<br \/>\n3<br \/>\n7<br \/>\n7<br \/>\n7<br \/>\n7<br \/>\n5<\/p>\n<p><center><a href=\"http:\/\/onlineclassesguru.com\/orders\/ordernow\"><img decoding=\"async\" src=\"https:\/\/encrypted-tbn0.gstatic.com\/images?q=tbn:ANd9GcTyj99p60XCLyLk1htB7-1neRt8-2QdnenNlQ&usqp=CAU\"target=\"_http:\/\/onlineclassesguru.com\/orders\/ordernow\"\/><\/center><p>","protected":false},"excerpt":{"rendered":"<p>Consider the system of equations Ax = b where the coecient matrix A has the following form. We used this example in class while trying to learn the row reduction algorithm. A = 2 6 6 6 6 4 123 456 789 3 7 7 7 7 5 1. Compute the null space of the&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-2613","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Matrices - onlineclassesguru<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/onlineclassesguru.com\/index.php\/2020\/10\/30\/matrices\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Matrices - onlineclassesguru\" \/>\n<meta property=\"og:description\" content=\"Consider the system of equations Ax = b where the coecient matrix A has the following form. We used this example in class while trying to learn the row reduction algorithm. A = 2 6 6 6 6 4 123 456 789 3 7 7 7 7 5 1. 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We used this example in class while trying to learn the row reduction algorithm. A = 2 6 6 6 6 4 123 456 789 3 7 7 7 7 5 1. 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