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Using elementary transformations, find the inverse of each of the matrices`[[2,-6],[ 1,-2]]` |
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Answer» Here, `A = [[2,-6],[1,-2]]` We know, `A = IA` `=>[[2,-6],[1,-2]] = [[1,0],[0,1]]A` Applying `C_2->C_2+3C_1` `=>[[2,0],[1,1]] = [[1,3],[0,1]]A` Applying `C_1->C_1-C_2` `=>[[2,0],[0,1]] = [[-2,3],[-1,1]]A` Applying `C_1->C_1/2` `=>[[1,0],[0,1]] = [[-1,3],[-1/2,1]]A` `=>I = [[-1,3],[-1/2,1]]A` Comparing it with , `I = A^-1A` So, `A^-1 = [[-1,3],[-1/2,1]]` |
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