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Using Elementary Row Transformations, Find the Inverse of the Matrix a = `[(1,2,3),(2,5,7),(-2,-4,-5)]` - Mathematics

Using elementary row transformations, find the inverse of the matrix A = `[(1,2,3),(2,5,7),(-2,-4,-5)]`

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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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