{"id":5061,"date":"2021-09-05T16:04:02","date_gmt":"2021-09-05T10:34:02","guid":{"rendered":"https:\/\/mathemerize.com\/?p=5061"},"modified":"2021-11-21T16:18:13","modified_gmt":"2021-11-21T10:48:13","slug":"determinants-of-matrix-4x4","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/determinants-of-matrix-4x4\/","title":{"rendered":"Determinants of Matrix 4×4 with Examples"},"content":{"rendered":"

Her you will learn how to find determinants of matrix 4×4 with example.<\/p>\n

Let’s begin –<\/p>\n

Determinants of Matrix 4×4<\/h2>\n

To evaluate the determinant of a square matrix of order 4 we follow the same procedure as discussed in previous post in evaluating the determinant of a square matrix of order 3.<\/p>\n

If A = \\(\\begin{bmatrix} a_{11} & a_{12} & a_{13} & a_{14} \\\\ a_{21} & a_{22} & a_{23} & a_{24} \\\\ a_{31} & a_{32} & a_{33} & a_{34} \\\\ a_{41} & a_{42} & a_{43} & a_{44} \\end{bmatrix}\\) is a square matrix of order 4,<\/p>\n

then | A | = \\(a_{11}\\begin{vmatrix} a_{22} & a_{23} & a_{24} \\\\ a_{32} & a_{33} & a_{34} \\\\\u00a0 a_{42} & a_{43} & a_{44} \\end{vmatrix}\\) – \\(a_{12}\\begin{vmatrix} a_{21} & a_{23} & a_{24} \\\\ a_{31} & a_{33} & a_{34} \\\\\u00a0 a_{41} & a_{43} & a_{44} \\end{vmatrix}\\) + \\(a_{13}\\begin{vmatrix} a_{21} & a_{22} & a_{24} \\\\ a_{31} & a_{32} & a_{34} \\\\\u00a0 a_{41} & a_{42} & a_{44} \\end{vmatrix}\\) – \\(a_{14}\\begin{vmatrix} a_{21} & a_{22} & a_{23} \\\\ a_{31} & a_{32} & a_{33} \\\\\u00a0 a_{41} & a_{42} & a_{43} \\end{vmatrix}\\)<\/p>\n

Example :<\/span><\/strong><\/h2>\n

Find the determinant of A = \\(\\begin{bmatrix} 1 & 2 & -1\u00a0 &\u00a0 3 \\\\ 2 & 1 & -2\u00a0 & 3\\\\ 3 & 1 & 2 & 1 \\\\ 1 & -1 & 0 & 2 \\end{bmatrix}\\).<\/p>\n

Solution<\/strong><\/span> : | A | = \\(\\begin{vmatrix} 1 & 2 & -1\u00a0 &\u00a0 3 \\\\ 2 & 1 & -2\u00a0 & 3\\\\ 3 & 1 & 2 & 1 \\\\ 1 & -1 & 0 & 2 \\end{vmatrix}\\)<\/p>\n

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

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

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

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

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

\\(\\implies\\) | A | = 1{(1)(4 – 0) – (-2)(2 + 1) + (3)(0 + 2)} – 2{(2)(4 – 0) – (-2)(6 – 1) + (3)(0 – 2)} – (-1){(2)(2 + 1) – (1)(6 – 1) + (3)(-3 – 1)} – 3{(2)(0 + 2) – (1)(0 – 2) + (-2)(-3 – 1)}<\/p>\n

\\(\\implies\\) | A | = 1(16) – 2(12) + (-1)(-11) – 3(14) = -39<\/p>\n\n\n

\n
Next – Properties of Determinant of Matrix<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Determinants of Matrix 3×3<\/a><\/div>\n<\/div>\n\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

Her you will learn how to find determinants of matrix 4×4 with example. Let’s begin – Determinants of Matrix 4×4 To evaluate the determinant of a square matrix of order 4 we follow the same procedure as discussed in previous post in evaluating the determinant of a square matrix of order 3. If A = …<\/p>\n

Determinants of Matrix 4×4 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":[210,221,211],"yoast_head":"\nDeterminants of Matrix 4x4 with Examples - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn how to find determinants of matrix 4x4 with example.\" \/>\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-4x4\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Determinants of Matrix 4x4 with Examples - 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