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Find the inverse of the matrix `A=[{:(1,3,3),(1,4,3),(1,3,4):}]` by using column transformations. |
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Answer» The given matrix is `A=[{:(1,3,3),(1,4,3),(1,3,4):}]` We know that, A = AI `[{:(1,3,3),(1,4,3),(1,3,4):}]=A[{:(1,0,0),(0,1,0),(0,0,1):}]` Applying `C_(2)toC_(2)-3C_(1),C_(3)toC_(3)-3C_(1),` we ,get `[{:(1,0,0),(1,1,0),(1,0,1):}]=A[{:(1,-3,-3),(0,1,0),(0,0,1):}]` Applying `C_(1)toC_(1)-C_(2)`, we get `[{:(1,0,0),(0,1,0),(1,0,1):}]=A[{:(4,-3,-3),(-1,1,0),(0,0,1):}]` Applying `C_(1)toC_(1)-C_(3)`, we get `[{:(1,0,0),(0,1,0),(0,0,1):}]=A[{:(7,-3,-3),(-1,1,0),(-1,0,1):}]` `A^(-1)=[{:(7,-3,-3),(-1,1,0),(-1,0,1):}]` |
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