{"id":5070,"date":"2021-09-05T16:34:54","date_gmt":"2021-09-05T11:04:54","guid":{"rendered":"https:\/\/mathemerize.com\/?p=5070"},"modified":"2021-11-21T16:06:09","modified_gmt":"2021-11-21T10:36:09","slug":"determinant-of-matrix-2x2","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/determinant-of-matrix-2x2\/","title":{"rendered":"Determinant of Matrix 2×2 with Examples"},"content":{"rendered":"

Here you will learn how to find the determinant of matrix 2×2 with examples.<\/p>\n

Let’s begin –<\/p>\n

Determinant of Matrix 2×2<\/h2>\n

If A = \\(\\begin{bmatrix} a_{11} & a_{12} \\\\ a_{21} & a_{22} \\end{bmatrix}\\) is a square matrix of 2×2,<\/p>\n

\n

then \\(a_{11}a_{22} – a_{12}a_{21}\\) is called the determinant of A.<\/p>\n

i.e. | A | = \\(\\begin{vmatrix} a_{11} & a_{12} \\\\ a_{21} & a_{22} \\end{vmatrix}\\)<\/p>\n

= \\(a_{11}a_{22} – a_{12}a_{21}\\)<\/p>\n<\/blockquote>\n

Thus, the determinant of a square matrix of order 2 is equal to the product of the diagonal elements minus the product of off-diagonal elements.<\/p>\n

Example 1<\/span><\/strong> : find the determinant of \\(\\begin{vmatrix} 5 & 4 \\\\ -2 & 3 \\end{vmatrix}\\).<\/p>\n

Solution <\/span><\/strong>:\u00a0Let | A | = \\(\\begin{vmatrix} 5 & 4 \\\\ -2 & 3 \\end{vmatrix}\\)<\/p>\n

By definition, we obtain<\/p>\n

| A | = ( \\(5\\times 3\\)) – (\\(4\\times -2\\)) = 15 + 8 = 23<\/p>\n

Example 2<\/span><\/strong> : find the determinant of \\(\\begin{vmatrix} sinx & cosx \\\\ -cosx & sinx \\end{vmatrix}\\).<\/p>\n

Solution <\/span><\/strong>:\u00a0\u00a0Let | A | = \\(\\begin{vmatrix} sinx & cosx \\\\ -cosx & sinx \\end{vmatrix}\\)<\/p>\n

By definition, we obtain<\/p>\n

| A | = ( \\(sin^2x\\)) – (\\(-cos^2x\\)) = \\(sin^2x\\) + \\(cos^2x\\) = 1<\/p>\n

Example 3<\/span><\/strong> : find the determinant of \\(\\begin{vmatrix} x – 1 & 1 \\\\ x^3 & x^2 + x + 1 \\end{vmatrix}\\).<\/p>\n

Solution <\/span><\/strong>: Let | A | = \\(\\begin{vmatrix} x – 1 & 1 \\\\ x^3 & x^2 + x + 1 \\end{vmatrix}\\)<\/p>\n

By definition, we obtain<\/p>\n

| A |\u00a0 = (x – 1)( \\(x^2 + x + 1\\)) – (\\(x^3\\))<\/p>\n

= \\(x^3 – 1\\) – \\(x^3\\) = -1<\/p>\n

Example 4<\/span><\/strong> : find the determinant of \\(\\begin{vmatrix} x^2 + xy + y^2 & x + y \\\\ x^2 – xy + y^2 & x – y \\end{vmatrix}\\).<\/p>\n

Solution <\/span><\/strong>: Let | A | = \\(\\begin{vmatrix} x^2 + xy + y^2 & x + y \\\\ x^2 – xy + y^2 & x – y \\end{vmatrix}\\)<\/p>\n

By definition, we obtain<\/p>\n

| A |\u00a0 = ( \\(x^2 + xy + y^2\\))(x – y) – (\\( x^2 – xy + y^2\\))(x + y)<\/p>\n

= (\\(x^3 – y^3\\)) – (\\(x^3 + y^3\\)) = \\(-2y^3\\)<\/p>\n

Example 5<\/span><\/strong> : find the determinant of \\(\\begin{vmatrix} 1 & log_ba \\\\ log_ab & 1 \\end{vmatrix}\\).<\/p>\n

Solution <\/span><\/strong>: Let | A | = \\(\\begin{vmatrix} 1 & log_ab \\\\ log_ab & 1 \\end{vmatrix}\\)<\/p>\n

By definition, we obtain<\/p>\n

| A |\u00a0 = 1 – ( \\(log_ab \\times log_ba\\)) = 1 – 1 = 0<\/p>\n\n\n

\n
Next – Determinants of Matrix 3\u00d73<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – How to Find the Determinant of Matrix<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn how to find the determinant of matrix 2×2 with examples. Let’s begin – Determinant of Matrix 2×2 If A = \\(\\begin{bmatrix} a_{11} & a_{12} \\\\ a_{21} & a_{22} \\end{bmatrix}\\) is a square matrix of 2×2, then \\(a_{11}a_{22} – a_{12}a_{21}\\) is called the determinant of A. i.e. | A | = \\(\\begin{vmatrix} …<\/p>\n

Determinant of Matrix 2×2 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":[210,209,211],"yoast_head":"\nDeterminant of Matrix 2x2 with Examples - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn how to find the determinant of matrix 2x2 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\/determinant-of-matrix-2x2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Determinant of Matrix 2x2 with Examples - 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