{"id":68,"date":"2009-05-30T21:35:21","date_gmt":"2009-05-31T04:35:21","guid":{"rendered":"http:\/\/new-gro.dyn.hhhh.org\/joeboy\/blog\/?p=68"},"modified":"2014-07-22T16:35:37","modified_gmt":"2014-07-22T23:35:37","slug":"problem-from-mathematical-quickies-94-%e2%80%9csimultaneous-equations%e2%80%9d","status":"publish","type":"post","link":"https:\/\/www.hhhh.org\/joeboy\/blog\/?p=68","title":{"rendered":"Problem from mathematical quickies &#8211; #94 &#8211; \u201cSimultaneous Equations\u201d"},"content":{"rendered":"<p>The problem is to solve an equation of 5 variables with 5 equations. Making it into a matrix the left side looks like an identity matrix. The first time I solved this I did it long hand &#8211; which took forever &#8211; then I took another look and saw what they person framing the problem was thinking. Which is cool since this trick should make it easier to attack matrix reduction for some annoying cases.\u00a0<\/p>\n<figure id=\"attachment_69\" aria-describedby=\"caption-attachment-69\" style=\"width: 390px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-69      \" title=\"simultaneous_equation_mathematical_quickies_numb94\" src=\"https:\/\/www.hhhh.org\/joeboy\/blog\/wp-content\/uploads\/2009\/05\/simultaneous_equation_mathematical_quickies_numb94.jpg\" alt=\"Solve the system of simultaneous equations\" width=\"390\" height=\"156\" \/><figcaption id=\"caption-attachment-69\" class=\"wp-caption-text\">Solve the system of simultaneous equations <\/figcaption><\/figure>\n<p>Sum all of the rows to create the new vector S. Then since all the\u00a0columns\u00a0of S have the same value it can be normalized so all the values of S are unity. Then by subtracting S from each of the rows (a..e) we create a new matrix M. Multiply M by negative 1 to keep the values at unit as opposed to negative unity and the solution is done. Most important it is done without the page of long hand reduction.\u00a0<\/p>\n<p style=\"text-align: center;\">\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-70\" title=\"simultaneous_equation_mathematical_quickies_numb94_answer\" src=\"https:\/\/www.hhhh.org\/joeboy\/blog\/wp-content\/uploads\/2009\/05\/simultaneous_equation_mathematical_quickies_numb94_answer.jpg\" alt=\"simultaneous_equation_mathematical_quickies_numb94_answer\" width=\"409\" height=\"191\" \/><\/a>\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The problem is to solve an equation of 5 variables with 5 equations. Making it into a matrix the left side looks like an identity matrix. The first time I solved this I did it long hand &#8211; which took forever &#8211; then I took another look and saw what they person framing the problem [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13,9],"tags":[],"class_list":["post-68","post","type-post","status-publish","format-standard","hentry","category-algerbra","category-math"],"_links":{"self":[{"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=\/wp\/v2\/posts\/68","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=68"}],"version-history":[{"count":9,"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=\/wp\/v2\/posts\/68\/revisions"}],"predecessor-version":[{"id":1179,"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=\/wp\/v2\/posts\/68\/revisions\/1179"}],"wp:attachment":[{"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=68"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=68"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.hhhh.org\/joeboy\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=68"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}