{"id":5059,"date":"2021-09-05T16:00:32","date_gmt":"2021-09-05T10:30:32","guid":{"rendered":"https:\/\/mathemerize.com\/?p=5059"},"modified":"2022-10-01T22:33:09","modified_gmt":"2022-10-01T17:03:09","slug":"determinants-of-matrix-3x3","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/determinants-of-matrix-3x3\/","title":{"rendered":"Determinants of Matrix 3×3 with Examples"},"content":{"rendered":"

Here you will learn how to find determinants of matrix 3×3 with examples.<\/p>\n

Let’s begin –<\/p>\n

Determinants of Matrix 3×3<\/h2>\n

If A = \\(\\begin{bmatrix} a_{11} & a_{12} & a_{13} \\\\ a_{21} & a_{22} & a_{23} \\\\ a_{31} & a_{32} & a_{33} \\end{bmatrix}\\) is a square matrix of order 3,<\/p>\n

then \\(a_{11}(a_{22}a_{33} – a_{23}a_{a32})\\) – \\(a_{12}(a_{33}a_{21} – a_{23}a_{31})\\) + \\(a_{13}(a_{32}a_{21} – a_{22}a_{31})\\) = 0 is defined as the determinant of A.<\/p>\n

i.e.\u00a0 | A | = \\(a_{11}\\begin{vmatrix} a_{22} & a_{23} \\\\ a_{32} & a_{33} \\end{vmatrix}\\) – \\(a_{12}\\begin{vmatrix} a_{21} & a_{23} \\\\ a_{31} & a_{33} \\end{vmatrix}\\) + \\(a_{13}\\begin{vmatrix} a_{21} & a_{22} \\\\ a_{31} & a_{32} \\end{vmatrix}\\)<\/p>\n

Example 1<\/span><\/strong> : find the determinant of A = \\(\\begin{bmatrix} 3 & -2 & 4 \\\\ 1 & 2 & 1 \\\\ 0 & 1 & -1 \\end{bmatrix}\\).<\/p>\n

Solution <\/span><\/strong>: | A | = \\(\\begin{vmatrix} 3 & -2 & 4 \\\\ 1 & 2 & 1 \\\\ 0 & 1 & -1 \\end{vmatrix}\\)<\/p>\n

\\(\\implies\\) | A | = \\(3\\begin{vmatrix} 2 & 1 \\\\ 1 & -1 \\end{vmatrix}\\) – \\((-2)\\begin{vmatrix} 1 & 1 \\\\ 0 & -1 \\end{vmatrix}\\) + \\(4\\begin{vmatrix} 1 & 2 \\\\ 0 & 1 \\end{vmatrix}\\)<\/p>\n

\\(\\implies\\) | A | = 3(-2 – 1) + 2(-1 – 0) + 4(1 – 0)\u00a0<\/p>\n

= -9 – 2 + 4 = -7<\/p>\n

Example 2<\/span><\/strong> : find the determinant of A = \\(\\begin{bmatrix} 1 & 2 & 3 \\\\ -4 & 3 & 6 \\\\ 2 & -7 & 9 \\end{bmatrix}\\).<\/p>\n

Solution <\/span><\/strong>:\u00a0 | A | = \\(\\begin{vmatrix} 1 & 2 & 3 \\\\ -4 & 3 & 6 \\\\ 2 & -7 & 9 \\end{vmatrix}\\)<\/p>\n

\\(\\implies\\) | A | = \\(1\\begin{vmatrix} 3 & 6 \\\\ -7 & 9 \\end{vmatrix}\\) – \\(2\\begin{vmatrix} -4 & 6 \\\\ 2 & 9 \\end{vmatrix}\\) + \\(3\\begin{vmatrix} -4 & 3 \\\\ 2 & -7 \\end{vmatrix}\\)<\/p>\n

\\(\\implies\\) | A | = (27 + 42) – 2(-36 – 12) + 3(28 – 6) = 231<\/p>\n

Note :<\/strong><\/p>\n

(1) Only square matrices have their determinants. The matrices which are not square do not have determinants.<\/p>\n

(2) The determinant of a square matrix of order 3 can be expanded along any row or column.<\/p>\n

(3) If a row or a column of a determinant consist of all zeros, then the value of the determinant is zero.<\/p>\n\n\n

\n
Next – Determinants of Matrix 4\u00d74<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Determinant of Matrix 2×2<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn how to find determinants of matrix 3×3 with examples. Let’s begin – Determinants of Matrix 3×3 If A = \\(\\begin{bmatrix} a_{11} & a_{12} & a_{13} \\\\ a_{21} & a_{22} & a_{23} \\\\ a_{31} & a_{32} & a_{33} \\end{bmatrix}\\) is a square matrix of order 3, then \\(a_{11}(a_{22}a_{33} – a_{23}a_{a32})\\) – \\(a_{12}(a_{33}a_{21} …<\/p>\n

Determinants of Matrix 3×3 with Examples<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","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":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[35],"tags":[210,222,211],"yoast_head":"\nDeterminants of Matrix 3x3 with Examples - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn how to find determinants of matrix 3x3 with examples.\" \/>\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\/determinants-of-matrix-3x3\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Determinants of Matrix 3x3 with Examples - 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