{"id":1742,"date":"2012-06-05T01:18:01","date_gmt":"2012-06-05T01:18:01","guid":{"rendered":"http:\/\/SchoolTutoring.com\/help\/?p=1742"},"modified":"2014-12-02T08:33:44","modified_gmt":"2014-12-02T08:33:44","slug":"addition-of-matrices","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/addition-of-matrices\/","title":{"rendered":"Addition of Matrices"},"content":{"rendered":"

Addition of matrices:<\/span><\/strong> If two matrices A and B are of\u00a0 the same order mxn, then the sum A+B is of the same order mxn and contains the elements obtained by adding the corresponding elements of A and B.<\/strong><\/p>\n

\"\"<\/p>\n

Scalar multiplication:<\/span><\/strong> If A is a matrix of order mxn and \u2018k\u2019 is a scalar then kA is a matrix of same order mxn whose elements are the products of k with the corresponding elements of A.<\/strong><\/p>\n

\"\"<\/p>\n

Here, \u00a0-A = (-1) A and so A-B = A+(-B)<\/strong><\/p>\n

Properties of matrix addition and multiplication:<\/span><\/strong><\/p>\n

a)\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong>Associative law: <\/strong><\/p>\n

A+(B+C) = (A+B)+C<\/strong><\/p>\n

\u00a0<\/strong><\/p>\n

b)\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong>Commutative law: <\/strong><\/p>\n

A + B = B + A.<\/strong><\/p>\n

\u00a0<\/strong><\/p>\n

c)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong>k(A+B) = kA + kB, where\u00a0 k is a scalar.<\/strong><\/p>\n

\u00a0<\/strong><\/p>\n

d)\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong>Law of identity:<\/strong><\/p>\n

If A is a matrix of order mxn and O is a null matrix of same order then<\/strong><\/p>\n

A+O = O+A = A, where O is called the additive identity.<\/strong><\/p>\n

\u00a0<\/strong><\/p>\n

e)\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong>Law of inverse: <\/strong><\/p>\n

If A is a matrix of order mxn then the additive inverse of A which is \u2013A is also of same order\u00a0 and A+(-A) = (-A)+A =O<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

Addition of matrices: If two matrices A and B are of\u00a0 the same order mxn, then the sum A+B is of the same order mxn and contains the elements obtained by adding the corresponding elements of A and B. Scalar multiplication: If A is a matrix of order mxn and \u2018k\u2019 is a scalar then […]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[50,907,969,1093,1159,1412,1587],"class_list":["post-1742","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-addition","tag-identity","tag-inverse","tag-matrix","tag-multiplication","tag-properties","tag-scalar"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/1742","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=1742"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/1742\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=1742"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=1742"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=1742"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}