{"id":185759,"date":"2025-01-23T05:41:27","date_gmt":"2025-01-23T05:41:27","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=185759"},"modified":"2025-01-23T05:41:29","modified_gmt":"2025-01-23T05:41:29","slug":"if-a-is-a-5x6-matrix-and-z-is-a-6-x5-zero-matrix-then-a-zt-a-select-one","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/23\/if-a-is-a-5x6-matrix-and-z-is-a-6-x5-zero-matrix-then-a-zt-a-select-one\/","title":{"rendered":"If A is a 5×6 matrix and Z is a 6 X5 zero matrix then A + Zt = A Select one"},"content":{"rendered":"\n

If A is a 5×6 matrix and Z is a 6 X5 zero matrix then A + Zt = A Select one:<\/p>\n\n\n\n

A True<\/p>\n\n\n\n

B False<\/p>\n\n\n\n

The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n

The correct answer is A: True<\/strong>.<\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

Let’s break down the problem step by step.<\/p>\n\n\n\n

    \n
  • Matrix A<\/strong> is a (5 \\times 6) matrix, which means it has 5 rows and 6 columns.<\/li>\n\n\n\n
  • Matrix Z<\/strong> is a (6 \\times 5) zero matrix, which means it has 6 rows and 5 columns and all its entries are zero.<\/li>\n<\/ul>\n\n\n\n

    The operation (Z^T) (transpose of Z):<\/h3>\n\n\n\n
      \n
    • The transpose of a matrix involves switching its rows and columns. So, the transpose of (Z), denoted (Z^T), will be a (5 \\times 6) matrix.<\/li>\n\n\n\n
    • Since (Z) is a zero matrix, all entries in (Z) are zero. Therefore, (Z^T) will also be a zero matrix with the same dimensions, i.e., a (5 \\times 6) zero matrix.<\/li>\n<\/ul>\n\n\n\n

      Matrix addition (A + Z^T):<\/h3>\n\n\n\n
        \n
      • Matrix (A) is a (5 \\times 6) matrix, and (Z^T) is also a (5 \\times 6) matrix (as we saw above). Since both matrices have the same dimensions, we can add them element-wise.<\/li>\n\n\n\n
      • Since (Z^T) is a zero matrix, adding it to (A) will not change the values of the entries in (A). The addition would look like:<\/li>\n<\/ul>\n\n\n\n

        [
        A + Z^T = A + \\text{(a matrix of zeros)} = A
        ]<\/p>\n\n\n\n

        Therefore, the expression (A + Z^T) equals matrix (A), which makes the statement True<\/strong>.<\/p>\n\n\n\n

        Conclusion:<\/h3>\n\n\n\n

        Since adding the zero matrix (which is the transpose of (Z)) to (A) doesn’t change (A), the correct answer is A: True<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"

        If A is a 5×6 matrix and Z is a 6 X5 zero matrix then A + Zt = A Select one: A True B False The Correct Answer and Explanation is : The correct answer is A: True. Explanation: Let’s break down the problem step by step. The operation (Z^T) (transpose of Z): Matrix […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-185759","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/185759","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=185759"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/185759\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=185759"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=185759"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=185759"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}