{"id":18802,"date":"2016-11-21T01:02:56","date_gmt":"2016-11-21T01:02:56","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=18802"},"modified":"2016-11-21T01:02:56","modified_gmt":"2016-11-21T01:02:56","slug":"linear-algebra-matrix-multiplication-no-cancellation-rule","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/linear-algebra-matrix-multiplication-no-cancellation-rule\/","title":{"rendered":"Linear algebra:  matrix multiplication:  no cancellation rule"},"content":{"rendered":"<h1>The tutor gives an example to show that with matrices, AB=AC doesn&#8217;t mean B=C.<\/h1>\n<p>Consider the matrices A, B, C, and D:<\/p>\n<p><img decoding=\"async\" src=\"\/..\/images\/matrices_nov20.png\" style=\"display:block;margin:auto\" \/><\/p>\n<p>By matrix multiplication, AB=AC.  (In fact, both products equal D.) Yet, obviously, B\u2260C. Matrix multiplication lacks the cancellation law that you see with the real numbers.<\/p>\n<p>HTH:)<\/p>\n<p>Source:<\/p>\n<p>Johnson\/Riess\/Arnold.  <u>Introduction to Linear Algebra<\/u>.  Don Mills:  Addison-Wesley, 1989.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The tutor gives an example to show that with matrices, AB=AC doesn&#8217;t mean B=C. Consider the matrices A, B, C, and D: By matrix multiplication, AB=AC. (In fact, both products equal D.) Yet, obviously, B\u2260C. Matrix multiplication lacks the cancellation &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/www.oracletutoring.ca\/blog\/linear-algebra-matrix-multiplication-no-cancellation-rule\/\"> <span class=\"screen-reader-text\">Linear algebra:  matrix multiplication:  no cancellation rule<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[302],"tags":[2039],"class_list":["post-18802","post","type-post","status-publish","format-standard","hentry","category-linear-algebra","tag-no-cancellation-law-in-matrix-multiplication"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/18802","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/comments?post=18802"}],"version-history":[{"count":5,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/18802\/revisions"}],"predecessor-version":[{"id":18807,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/18802\/revisions\/18807"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=18802"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=18802"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=18802"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}