{"id":367,"date":"2018-07-12T09:06:55","date_gmt":"2018-07-12T09:06:55","guid":{"rendered":"http:\/\/itp15.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=367"},"modified":"2019-05-15T09:06:40","modified_gmt":"2019-05-15T09:06:40","slug":"systems-of-linear-equations-direct-methods-2","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/itp15\/chapter\/systems-of-linear-equations-direct-methods-2\/","title":{"rendered":"Systems of Linear equations: Direct Methods-2"},"content":{"raw":"<div><span style=\"float: right;\"><a href=\"https:\/\/youtu.be\/LAdeGQs0Cbg\" target=\"_blank\" rel=\"noopener\"><img src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a>\r\n<\/span><\/div>\r\n<p style=\"text-align: center;\"><strong>Systems of Linear equations: Direct Methods-2<\/strong><\/p>\r\n&nbsp;\r\n\r\n&nbsp;\r\n<p style=\"text-align: left;\"><img class=\"aligncenter wp-image-376 size-full\" src=\"http:\/\/itp15.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/26\/2018\/07\/1506670230Module-29-sys-of-eqs-direct-methods_Page_1-e1533212690535.jpg\" alt=\"\" width=\"1284\" height=\"1731\" \/> <img class=\"aligncenter wp-image-375 size-full\" src=\"http:\/\/itp15.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/26\/2018\/07\/1506670230Module-29-sys-of-eqs-direct-methods_Page_2-e1533212706532.jpg\" alt=\"\" width=\"1315\" height=\"1982\" \/> <img class=\"aligncenter wp-image-374 size-full\" src=\"http:\/\/itp15.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/26\/2018\/07\/1506670230Module-29-sys-of-eqs-direct-methods_Page_3-e1533212731306.jpg\" alt=\"\" width=\"1315\" height=\"1812\" \/> <img class=\"aligncenter wp-image-373 size-full\" src=\"http:\/\/itp15.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/26\/2018\/07\/1506670230Module-29-sys-of-eqs-direct-methods_Page_4-e1533212754614.jpg\" alt=\"\" width=\"1303\" height=\"1953\" \/> <img class=\"aligncenter wp-image-372 size-full\" src=\"http:\/\/itp15.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/26\/2018\/07\/1506670230Module-29-sys-of-eqs-direct-methods_Page_5-e1533212795369.jpg\" alt=\"\" width=\"1298\" height=\"1947\" \/> <img class=\"aligncenter wp-image-371 size-full\" src=\"http:\/\/itp15.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/26\/2018\/07\/1506670230Module-29-sys-of-eqs-direct-methods_Page_6-e1533212821734.jpg\" alt=\"\" width=\"1344\" height=\"1958\" \/> <img class=\"aligncenter wp-image-370 size-full\" src=\"http:\/\/itp15.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/26\/2018\/07\/1506670230Module-29-sys-of-eqs-direct-methods_Page_7-e1533212847624.jpg\" alt=\"\" width=\"1303\" height=\"1947\" \/> <img class=\"aligncenter wp-image-369 size-full\" src=\"http:\/\/itp15.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/26\/2018\/07\/1506670230Module-29-sys-of-eqs-direct-methods_Page_8-e1533212868864.jpg\" alt=\"\" width=\"1309\" height=\"1871\" \/> <img class=\"alignnone wp-image-368 size-full\" src=\"http:\/\/itp15.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/26\/2018\/07\/1506670230Module-29-sys-of-eqs-direct-methods_Page_9-e1533212912821.jpg\" alt=\"\" width=\"1309\" height=\"1648\" \/><\/p>\r\n<strong>Additional Reading material<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify;\"><span style=\"text-align: justify; font-size: 1em;\">The following are some of the references on Matrix Algebra, Systems of Linear equations, Numerical methods for solutions of the linear systems. The detailed discussion on the methods, algorithms and related results presented in this module can be found to some extent in the references [1], [2], [11] and [13].<\/span><\/p>\r\n\r\n<div>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>you can view video on Systems of Linear equations: Direct Methods-2<\/strong><\/td>\r\n<td><a href=\"https:\/\/youtu.be\/LAdeGQs0Cbg\" target=\"_blank\" rel=\"noopener\"><img class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<strong>References:<\/strong>\r\n\r\n&nbsp;\r\n\r\n1.\u00a0\u00a0\u00a0 Steven C Chapra &amp; Raymond Canale: Numerical Methods for Engineers, 5th Ed. TMH, 2009\r\n\r\n2.\u00a0\u00a0 Conte Samuel D. &amp; Carl de Boor: Elementary N A \u2013 An Algorithmic approach, 3rd Ed., TMH, 2005.\r\n\r\n3.\u00a0 \u00a0Alfio Quarteroni, Recardo Sacco, Fausto Saleri: N. Mathematics (Text in Applied Math.) 2nd Ed. SV, 2007\r\n\r\n4.\u00a0\u00a0 Richard L. Burden &amp; J. Douglas Faires: N A \u2013Theory &amp; Applications, Cengage Learning, 2005.\r\n\r\n5.\u00a0 \u00a0Won Y. Yang, Wenwu Cao, Tae-Sang Chung, &amp; John Morris: Applied NM Using Matlab, WSE, 2005\r\n\r\n6.\u00a0 \u00a0Kendall Atkinson &amp; Weimin Han: Elimentary Numerical Analysis, Third edition, Wiley Dreamtech India(P) Ltd., 2004.\r\n\r\n7.\u00a0 \u00a0Matheus Grasselli &amp; Dimitry Pelinovsky: Numerical Mathematics, Narosa Publishing House, 2009.\r\n\r\n8.\u00a0\u00a0 s. s. ssatry: Introductory Methods of Numerical Analysis, PHI, 1989.\r\n\r\n9.\u00a0\u00a0 Polynomial interpolation, From Wikipedia, the free encyclopaedia\r\n\r\n10.\u00a0 Carl-Erik Froberg: Introduction to Numerical Analysis, Addition-Wesley Pub. Co., 1981.\r\n\r\n11.\u00a0 \u00a0Rao V. Dukkipati: Numerical Methods, NEW AGE INTERNATIONAL (P) LIMITED, PUBLISHERS, 2010.\r\n\r\n<span style=\"font-size: 1em;\">12.\u00a0 Robert J. Schilling &amp; Sandra L. Harris: \u00a0Applied Numerical Methods for Engineers, Thomson Brooks\/Kole, 1999.<\/span>\r\n\r\n<span style=\"font-size: 1em;\">13.\u00a0 Erwin Kreyszig: Advanced Engineering Mathematics, Jhon Wiley &amp; Sons Inc., 2011.<\/span>\r\n\r\n<\/div>","rendered":"<div><span style=\"float: right;\"><a href=\"https:\/\/youtu.be\/LAdeGQs0Cbg\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a><br \/>\n<\/span><\/div>\n<p style=\"text-align: center;\"><strong>Systems of Linear equations: Direct Methods-2<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: left;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-376 size-full\" src=\"http:\/\/itp15.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/26\/2018\/07\/1506670230Module-29-sys-of-eqs-direct-methods_Page_1-e1533212690535.jpg\" alt=\"\" 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https:\/\/ebooks.inflibnet.ac.in\/itp15\/wp-content\/uploads\/sites\/26\/2018\/07\/1506670230Module-29-sys-of-eqs-direct-methods_Page_8-e1533212868864-65x93.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/itp15\/wp-content\/uploads\/sites\/26\/2018\/07\/1506670230Module-29-sys-of-eqs-direct-methods_Page_8-e1533212868864-225x322.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/itp15\/wp-content\/uploads\/sites\/26\/2018\/07\/1506670230Module-29-sys-of-eqs-direct-methods_Page_8-e1533212868864-350x500.jpg 350w\" sizes=\"auto, (max-width: 1309px) 100vw, 1309px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-368 size-full\" src=\"http:\/\/itp15.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/26\/2018\/07\/1506670230Module-29-sys-of-eqs-direct-methods_Page_9-e1533212912821.jpg\" alt=\"\" width=\"1309\" height=\"1648\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/itp15\/wp-content\/uploads\/sites\/26\/2018\/07\/1506670230Module-29-sys-of-eqs-direct-methods_Page_9-e1533212912821.jpg 1309w, https:\/\/ebooks.inflibnet.ac.in\/itp15\/wp-content\/uploads\/sites\/26\/2018\/07\/1506670230Module-29-sys-of-eqs-direct-methods_Page_9-e1533212912821-238x300.jpg 238w, https:\/\/ebooks.inflibnet.ac.in\/itp15\/wp-content\/uploads\/sites\/26\/2018\/07\/1506670230Module-29-sys-of-eqs-direct-methods_Page_9-e1533212912821-768x967.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/itp15\/wp-content\/uploads\/sites\/26\/2018\/07\/1506670230Module-29-sys-of-eqs-direct-methods_Page_9-e1533212912821-813x1024.jpg 813w, https:\/\/ebooks.inflibnet.ac.in\/itp15\/wp-content\/uploads\/sites\/26\/2018\/07\/1506670230Module-29-sys-of-eqs-direct-methods_Page_9-e1533212912821-65x82.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/itp15\/wp-content\/uploads\/sites\/26\/2018\/07\/1506670230Module-29-sys-of-eqs-direct-methods_Page_9-e1533212912821-225x283.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/itp15\/wp-content\/uploads\/sites\/26\/2018\/07\/1506670230Module-29-sys-of-eqs-direct-methods_Page_9-e1533212912821-350x441.jpg 350w\" sizes=\"auto, (max-width: 1309px) 100vw, 1309px\" \/><\/p>\n<p><strong>Additional Reading material<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"text-align: justify; font-size: 1em;\">The following are some of the references on Matrix Algebra, Systems of Linear equations, Numerical methods for solutions of the linear systems. The detailed discussion on the methods, algorithms and related results presented in this module can be found to some extent in the references [1], [2], [11] and [13].<\/span><\/p>\n<div>\n<table>\n<tbody>\n<tr>\n<td><strong>you can view video on Systems of Linear equations: Direct Methods-2<\/strong><\/td>\n<td><a href=\"https:\/\/youtu.be\/LAdeGQs0Cbg\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>References:<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>1.\u00a0\u00a0\u00a0 Steven C Chapra &amp; Raymond Canale: Numerical Methods for Engineers, 5th Ed. TMH, 2009<\/p>\n<p>2.\u00a0\u00a0 Conte Samuel D. &amp; Carl de Boor: Elementary N A \u2013 An Algorithmic approach, 3rd Ed., TMH, 2005.<\/p>\n<p>3.\u00a0 \u00a0Alfio Quarteroni, Recardo Sacco, Fausto Saleri: N. Mathematics (Text in Applied Math.) 2nd Ed. SV, 2007<\/p>\n<p>4.\u00a0\u00a0 Richard L. Burden &amp; J. Douglas Faires: N A \u2013Theory &amp; Applications, Cengage Learning, 2005.<\/p>\n<p>5.\u00a0 \u00a0Won Y. Yang, Wenwu Cao, Tae-Sang Chung, &amp; John Morris: Applied NM Using Matlab, WSE, 2005<\/p>\n<p>6.\u00a0 \u00a0Kendall Atkinson &amp; Weimin Han: Elimentary Numerical Analysis, Third edition, Wiley Dreamtech India(P) Ltd., 2004.<\/p>\n<p>7.\u00a0 \u00a0Matheus Grasselli &amp; Dimitry Pelinovsky: Numerical Mathematics, Narosa Publishing House, 2009.<\/p>\n<p>8.\u00a0\u00a0 s. s. ssatry: Introductory Methods of Numerical Analysis, PHI, 1989.<\/p>\n<p>9.\u00a0\u00a0 Polynomial interpolation, From Wikipedia, the free encyclopaedia<\/p>\n<p>10.\u00a0 Carl-Erik Froberg: Introduction to Numerical Analysis, Addition-Wesley Pub. Co., 1981.<\/p>\n<p>11.\u00a0 \u00a0Rao V. Dukkipati: Numerical Methods, NEW AGE INTERNATIONAL (P) LIMITED, PUBLISHERS, 2010.<\/p>\n<p><span style=\"font-size: 1em;\">12.\u00a0 Robert J. Schilling &amp; Sandra L. Harris: \u00a0Applied Numerical Methods for Engineers, Thomson Brooks\/Kole, 1999.<\/span><\/p>\n<p><span style=\"font-size: 1em;\">13.\u00a0 Erwin Kreyszig: Advanced Engineering Mathematics, Jhon Wiley &amp; Sons Inc., 2011.<\/span><\/p>\n<\/div>\n","protected":false},"author":4,"menu_order":30,"template":"","meta":{"_acf_changed":false,"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["dr-v-d-pathak"],"pb_section_license":""},"chapter-type":[],"contributor":[59],"license":[],"class_list":["post-367","chapter","type-chapter","status-publish","hentry","contributor-dr-v-d-pathak"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/itp15\/wp-json\/pressbooks\/v2\/chapters\/367","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/itp15\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/itp15\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/itp15\/wp-json\/wp\/v2\/users\/4"}],"version-history":[{"count":6,"href":"https:\/\/ebooks.inflibnet.ac.in\/itp15\/wp-json\/pressbooks\/v2\/chapters\/367\/revisions"}],"predecessor-version":[{"id":613,"href":"https:\/\/ebooks.inflibnet.ac.in\/itp15\/wp-json\/pressbooks\/v2\/chapters\/367\/revisions\/613"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/itp15\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/itp15\/wp-json\/pressbooks\/v2\/chapters\/367\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/itp15\/wp-json\/wp\/v2\/media?parent=367"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/itp15\/wp-json\/pressbooks\/v2\/chapter-type?post=367"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/itp15\/wp-json\/wp\/v2\/contributor?post=367"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/itp15\/wp-json\/wp\/v2\/license?post=367"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}