Give an example of a 2×2 matrix whose is determinant is 13<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n A 2×2 matrix is typically represented as:<\/p>\n\n\n\n [ The determinant ( \\text{det}(A) ) of a 2×2 matrix is calculated using the formula:<\/p>\n\n\n\n [ For the determinant to be 13, we need to find values for ( a ), ( b ), ( c ), and ( d ) such that the equation ( ad – bc = 13 ) holds true.<\/p>\n\n\n\n Let’s consider the matrix:<\/p>\n\n\n\n [ We will now calculate the determinant:<\/p>\n\n\n\n [ [ This is not the desired determinant. Now, let’s adjust the values.<\/p>\n\n\n\n Let’s try the matrix:<\/p>\n\n\n\n [ Now calculate the determinant:<\/p>\n\n\n\n [ [ Again, the determinant is 14, not 13. Let’s change the matrix further.<\/p>\n\n\n\n Consider the matrix:<\/p>\n\n\n\n [ Now, we calculate the determinant:<\/p>\n\n\n\n [ [ Thus, the determinant of the matrix:<\/p>\n\n\n\n [ is indeed 13.<\/p>\n\n\n\n The determinant of a 2×2 matrix is a scalar value that can be used to determine several important properties of the matrix. A non-zero determinant, like 13 in this case, indicates that the matrix is invertible<\/strong> (i.e., it has an inverse matrix). The determinant also gives information about the area scaling factor when the matrix is applied as a linear transformation to a unit square. A determinant of 13 means that the transformation scales areas by a factor of 13.<\/p>\n","protected":false},"excerpt":{"rendered":" Give an example of a 2×2 matrix whose is determinant is 13 The Correct Answer and Explanation is: A 2×2 matrix is typically represented as: [A = \\begin{bmatrix} a & b \\ c & d \\end{bmatrix}] The determinant ( \\text{det}(A) ) of a 2×2 matrix is calculated using the formula: [\\text{det}(A) = ad – bc] […]<\/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-165112","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/165112","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=165112"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/165112\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=165112"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=165112"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=165112"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
A = \\begin{bmatrix} a & b \\ c & d \\end{bmatrix}
]<\/p>\n\n\n\n
\\text{det}(A) = ad – bc
]<\/p>\n\n\n\nExample of a matrix:<\/h3>\n\n\n\n
A = \\begin{bmatrix} 4 & 3 \\ 2 & 5 \\end{bmatrix}
]<\/p>\n\n\n\n
\\text{det}(A) = (4)(5) – (3)(2)
]<\/p>\n\n\n\n
\\text{det}(A) = 20 – 6 = 14
]<\/p>\n\n\n\nNew matrix example:<\/h3>\n\n\n\n
A = \\begin{bmatrix} 5 & 2 \\ 3 & 4 \\end{bmatrix}
]<\/p>\n\n\n\n
\\text{det}(A) = (5)(4) – (2)(3)
]<\/p>\n\n\n\n
\\text{det}(A) = 20 – 6 = 14
]<\/p>\n\n\n\nCorrect matrix:<\/h3>\n\n\n\n
A = \\begin{bmatrix} 7 & 4 \\ 1 & 3 \\end{bmatrix}
]<\/p>\n\n\n\n
\\text{det}(A) = (7)(3) – (4)(1)
]<\/p>\n\n\n\n
\\text{det}(A) = 21 – 4 = 13
]<\/p>\n\n\n\n
A = \\begin{bmatrix} 7 & 4 \\ 1 & 3 \\end{bmatrix}
]<\/p>\n\n\n\nExplanation:<\/h3>\n\n\n\n