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Find the matrix A satisfying the matrix equation: `[[2,1],[3,2]]` A`[[-3,2],[5,-3]]`=`[[1,0],[0,1]]` |
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Answer» `[[2,1],[3,2]]A[[-3,2],[5,-3]] = [[1,0],[0,1]]` Let `B = [[2,1],[3,2]]` `C = [[-3,2],[5,-3]]` Then, `BAC = I` `=>B^-1BAC^-1C = B^-1C^-1I` `=>A = B^-1C^-1 = (CB)^-1` Now, `CB = [[-3,2],[5,-3]][[2,1],[3,2]] = [[0,1],[1,-1]]` Now, `(CB)^-1 = (adj(CB))/|CB|` `=>adj(CB) = [[-1,-1],[-1,0]]` `=>|CB| = 0-1 = -1` `:. (CB)^-1 = [[1,1],[1,0]]` `:. A = (CB)^-1 = [[1,1],[1,0]]` |
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