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Question
Using elementary row transformations, find the inverse of the matrix A = `[(1,2,3),(2,5,7),(-2,-4,-5)]`
Solution
We know that
A = IA
i.e `[(1,2,3),(2,5,7),(-2,-4,-5)] = A[(1,0,0),(0,1,0),(0,0,1)]`
Applying R2→ R2−2R1 and R3→R3 +2R1
`=> [(1,2,3),(0,1,1),(0,0,1)] = A[(1,0,0),(-2,1,0),(2,0,1)]`
Applying R1→R1−2R2
`=> [(1,0,1),(0,1,1),(0,0,1)] = A [(5,-2,0),(-2,1,0),(2,0,1)]`
Applying R1→R1−R3
`=>[(1,0,0),(0,1,1),(0,0,1)] = A[(3,-2,-1),(-2,1,0),(2,0,1)]`
Applying R2→R2−R3
`=> [(1,0,0),(0,1,0),(0,0,1)] = A [(3,-2,-1),(-4,1,-1),(2,0,1)]`
Hence `A^(-1) = [(3,-2,-1),(-4,1,-1),(2,0,1)]`
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