{"id":10021,"date":"2022-02-09T16:40:26","date_gmt":"2022-02-09T11:10:26","guid":{"rendered":"https:\/\/mathemerize.com\/?p=10021"},"modified":"2022-02-09T16:41:14","modified_gmt":"2022-02-09T11:11:14","slug":"singular-matrix-definition-examples-and-determinant","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/singular-matrix-definition-examples-and-determinant\/","title":{"rendered":"Singular Matrix – Definition, Examples and Determinant"},"content":{"rendered":"

Here you will learn what is singular matrix definition with examples and also determinant of singular matrix.<\/p>\n

Let’s begin –<\/p>\n

Singular Matrix<\/h2>\n

Definition<\/strong> : A square matrix is a singular matrix if its determinant<\/strong> is zero.<\/p>\n

Otherwise, it is a non-singular matrix.<\/p><\/blockquote>\n

Also Read : How to Find the Determinant of Matrix<\/a><\/p>\n

Example<\/strong><\/span> : Show that the matrix A = \\(\\begin{bmatrix} 1 & -3 & 4 \\\\ -5 &\u00a0 2 & 2 \\\\ 4 & 1 &\u00a0 -6\u00a0 \\end{bmatrix}\\) is singular ?<\/p>\n

Solution<\/span><\/strong> : The matrix A is singular, if<\/p>\n

|A| = 0<\/p>\n

\\(\\implies\\)\u00a0 |A| = \\(\\begin{bmatrix} 1 & -3 & 4 \\\\ -5 &\u00a0 2 & 2 \\\\ 4 & 1 &\u00a0 -6\u00a0 \\end{bmatrix}\\)<\/p>\n

= 1 \\(\\begin{vmatrix} 2 & 2 \\\\ 1 &\u00a0 -6\u00a0 \\end{vmatrix}\\) – ( -3) \\(\\begin{vmatrix} -5 & 2 \\\\ 4 &\u00a0 -6\u00a0 \\end{vmatrix}\\) + 4 \\(\\begin{vmatrix} -5 & 2 \\\\ 4 & 1\u00a0 \\end{vmatrix}\\)<\/p>\n

= 1(-12 – 2) + 3(30 – 8) + 4(-5 – 8)<\/p>\n

= -14 + 66 – 52<\/p>\n

= 0<\/p>\n

\\(\\implies\\) |A| = 0,<\/p>\n

Hence, Matrix A is singular.<\/p>\n

Example<\/strong><\/span> : For what value of x the matrix A = \\(\\begin{bmatrix} 1 & -2 & 3 \\\\ 1 &\u00a0 2 & 1 \\\\ x & 2 &\u00a0 -3\u00a0 \\end{bmatrix}\\) is singular ?<\/p>\n

Solution<\/span><\/strong> : The matrix A is singular, if<\/p>\n

|A| = 0<\/p>\n

\\(\\implies\\)\u00a0 \\(\\begin{vmatrix} 1 & -2 & 3 \\\\ 1 &\u00a0 2 & 1 \\\\ x & 2 &\u00a0 -3\u00a0 \\end{vmatrix}\\) = 0<\/p>\n

\\(\\implies\\)\u00a0 1 \\(\\begin{vmatrix} 2 & 1 \\\\ 2 &\u00a0 -3\u00a0 \\end{vmatrix}\\) + 2 \\(\\begin{vmatrix} 1 & 1 \\\\ x &\u00a0 -3\u00a0 \\end{vmatrix}\\) + 3 \\(\\begin{vmatrix} 1 & 2 \\\\ x &\u00a0 2\u00a0 \\end{vmatrix}\\) = 0<\/p>\n

\\(\\implies\\)\u00a0 (-6 – 2) + 2(-3 – x) + 3(2 – 2x) = 0<\/p>\n

\\(\\implies\\)\u00a0 -8 – 6 – 2x + 6 – 6x = 0<\/p>\n

\\(\\implies\\)\u00a0 -8x – 8 = 0\u00a0 \\(\\implies\\) x = -1<\/p>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what is singular matrix definition with examples and also determinant of singular matrix. Let’s begin – Singular Matrix Definition : A square matrix is a singular matrix if its determinant is zero. Otherwise, it is a non-singular matrix. Also Read : How to Find the Determinant of Matrix Example : Show …<\/p>\n

Singular Matrix – Definition, Examples and Determinant<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[35,34],"tags":[886,887,888],"yoast_head":"\nSingular Matrix - Definition, Examples and Determinant<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is singular matrix definition with examples and also determinant of singular matrix.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/singular-matrix-definition-examples-and-determinant\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Singular Matrix - 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