{"id":7382,"date":"2022-03-21T14:54:23","date_gmt":"2022-03-21T09:24:23","guid":{"rendered":"https:\/\/www.goseeko.com\/blog\/?p=7382"},"modified":"2022-03-21T14:54:27","modified_gmt":"2022-03-21T09:24:27","slug":"elementary-transformation-of-a-matrix","status":"publish","type":"post","link":"https:\/\/www.goseeko.com\/blog\/elementary-transformation-of-a-matrix\/","title":{"rendered":"Elementary transformation of a matrix"},"content":{"rendered":"\n

When we apply any of the following operation on a matrix, then we call it an elementary transformation<\/a>.<\/p>\n\n\n\n

1. <\/strong>Interchanging any two rows (or columns). This transformation is indicated by , <\/em>if the i<\/em>th and j<\/em>th rows are interchanged.<\/p>\n\n\n\n

2. <\/strong>Multiplication of the elements of any row \u00a0 <\/em>(or column) by a non-zero scalar quantity k <\/em>is denoted by (k<\/em>.).<\/p>\n\n\n\n

3. <\/strong>Addition of constant multiplication of the elements of any row  <\/em>to the corresponding elements of any other row Rj <\/em>is denoted by ( <\/em><\/em>+ k<\/em><\/em>).<\/p>\n\n\n\n

If a matrix B <\/em>is obtained from a matrix A <\/em>by one or more E-operations, then B <\/em>will be equivalent to A. <\/em>We use the symbol ~ for equivalence.<\/p>\n\n\n\n

i.e.<\/em>, A <\/em>~ B<\/em>.<\/p>\n\n\n\n

Inverse of a matrix by using el<\/strong>. transformation-<\/strong><\/p>\n\n\n\n

The following transformations are elementary transformations-<\/p>\n\n\n\n

1. Interchange of any two rows (column)<\/p>\n\n\n\n

2. Multiplication of any row or column by any non-zero scalar quantity k.<\/p>\n\n\n\n

3. Addition to one row (column) of another row(column) multiplied by any non-zero scalar.<\/p>\n\n\n\n

The symbol ~ we use for equivalence.<\/p>\n\n\n\n

Elementary matrices<\/strong><\/h2>\n\n\n\n

If we get a square matrix from an identity or unit matrix by using any single el. transformation, we call it an elementary matrix.<\/p>\n\n\n\n

Note- Every elementary row transformation of a matrix can affect by pre-multiplication with the corresponding elementary matrix.<\/p>\n\n\n\n

The method of finding inverse of a non-singular matrix by using el<\/strong>. transformation-<\/strong><\/p>\n\n\n\n

Working steps-<\/p>\n\n\n\n

1. Write A = IA<\/p>\n\n\n\n

2. Perform an elementary row transformation of A on the left side and I on the right side.<\/p>\n\n\n\n

3. Apply elementary row transformation until \u2018A\u2019 (left side) reduces to I, then I reduces to .<\/p>\n\n\n\n

Example-1: Find the inverse of matrix \u2018A\u2019 by using elementary transformation<\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Sol.  <\/strong>Write the matrix \u2018A\u2019 as-  <\/p>\n\n\n\n

A = IA<\/p>\n\n\n\n

Now apply the following operation<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n\n\n\n

So that<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Example-2: Find the inverse of matrix \u2018A\u2019 by using el<\/strong>. transformation-<\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Sol.\u00a0 Write the given matrix \u2018A\u2019 as-\u00a0\u00a0<\/p>\n\n\n\n

hence A = IA<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n\n\n\n

So that<\/p>\n\n\n\n

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

When we apply any of the following operation on a matrix, then it is called an elementary transformation.<\/p>\n","protected":false},"author":28,"featured_media":7389,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[31],"tags":[],"class_list":["post-7382","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-maths"],"yoast_head":"\nElementary transformation of a matrix - Goseeko blog<\/title>\n<meta name=\"description\" content=\"When we apply any of the following operation on a matrix, then it is called an elementary transformation.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.goseeko.com\/blog\/elementary-transformation-of-a-matrix\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Elementary transformation of a matrix - 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