\n| \n \u00ae31<\/p>\n<\/td>\n | \n \u00ae32<\/p>\n<\/td>\n | \n \u00ae33<\/p>\n<\/td>\n<\/tr>\n<\/table>\n Figure 1.9 Calculating the inverse of a matrix. To calculate the inverse of a matrix, you first find its accompanying cofactor matrix, and then divide it by the determinant of the original matrix.<\/p>\n In order to use that formula, you need to know how to calculate cofactors of the elements of the matrices. The principle is simple; you cross out the ith column and the jthrow. Therefore, if the element is M, you would cross out the first row and the first column, leaving a 2×2 matrix. This is called the minor of the element. Now, you take the 2×2 matrix and calculate the determinant of it; the result of that determi\u00adnant is called the cofactor. See Figure 1.10 for more details.<\/p>\n Now for the last step. Take your newly found cofactor matrix and multiply it by one over the determinant of the original matrix. The determinant in this case is -17, so you multiply the cofactor matrix by — 1\/17. By doing this, you have the final inverted matrix, as shown in Figure 1.11.<\/p>\n <\/p>\n <\/p>\n \n\n| \n 3 2 3<\/p>\n 4 5 5 7 1 3<\/p>\n 5 5 1 3<\/p>\n 3 2 3 1<\/p>\n<\/td>\n<\/tr>\n<\/table>\n <\/p>\n \n\n| \n M =<\/p>\n<\/td>\n<\/tr>\n<\/table>\n <\/p>\n \n\n| \n = (5×3-1 x 5) = 10<\/p>\n<\/td>\n<\/tr>\n<\/table>\n <\/p>\n \n\n| \n \u00a911 \u2014<\/p>\n<\/td>\n<\/tr>\n<\/table>\n <\/p>\n \n\n| \n -55<\/p>\n — 1 3<\/p>\n — 2 3<\/p>\n — 1 3<\/p>\n<\/td>\n<\/tr>\n<\/table>\n <\/p>\n \n\n| \n = (3 x 1 — 3 x 2) = -3<\/p>\n<\/td>\n<\/tr>\n<\/table>\n <\/p>\n \n\n| \n \u00a912 \u2014<\/p>\n<\/td>\n<\/tr>\n<\/table>\n <\/p>\n<\/p>\n<\/p>\n<\/p>\n<\/p>\n<\/p>\n <\/p>\n 10 -3 -5 23 -12 -3 -3111 7<\/p>\n Figure 1.10 Calculating cofactors. Top:The original matrix.<\/p>\n \n\n| \n 1<\/p>\n -17<\/p>\n<\/td>\n<\/tr>\n<\/table>\n Middle: Calculating two of the cofactors. Bottom: The matrix with all its cofactors calculated.<\/p>\n \n\n| \n ~10 -3<\/p>\n<\/td>\n | \n -5~<\/p>\n<\/td>\n | \n<\/td>\n | \n -0.588<\/p>\n<\/td>\n | \n 0.176<\/p>\n<\/td>\n | \n 0.294 ~<\/p>\n<\/td>\n<\/tr>\n | \n| \n 23 -12<\/p>\n<\/td>\n | \n -3<\/p>\n<\/td>\n | \n —<\/p>\n<\/td>\n | \n -1.353<\/p>\n<\/td>\n | \n 0.706<\/p>\n<\/td>\n | \n 0.177<\/p>\n<\/td>\n<\/tr>\n | \n| \n -31 11<\/p>\n<\/td>\n | \n 7<\/p>\n<\/td>\n | \n<\/td>\n | \n 1.824<\/p>\n<\/td>\n | \n -0.647<\/p>\n<\/td>\n | \n -0.418<\/p>\n<\/td>\n<\/tr>\n<\/table>\n Figure I. II Calculating the inverse of a matrix using the process described in the previous section\u2014results are rounded to three decimal places to save space.<\/p>\n","protected":false},"excerpt":{"rendered":" Hey, what do you know, the last part of the matrix section is here already. That wasn\u2019t so bad was it? This section is on the inverse of a matrix. The inverse of a matrix satisfies the following equation: M(M-1) = I. M is the original matrix, M-1 is the inverse of M, and I […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[7],"tags":[],"_links":{"self":[{"href":"https:\/\/3dbym.ru\/wp-json\/wp\/v2\/posts\/39"}],"collection":[{"href":"https:\/\/3dbym.ru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/3dbym.ru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/3dbym.ru\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/3dbym.ru\/wp-json\/wp\/v2\/comments?post=39"}],"version-history":[{"count":0,"href":"https:\/\/3dbym.ru\/wp-json\/wp\/v2\/posts\/39\/revisions"}],"wp:attachment":[{"href":"https:\/\/3dbym.ru\/wp-json\/wp\/v2\/media?parent=39"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/3dbym.ru\/wp-json\/wp\/v2\/categories?post=39"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/3dbym.ru\/wp-json\/wp\/v2\/tags?post=39"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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