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# Using Elementary Row Transformations, Find the Inverse of the Matrix a = [(1,2,3),(2,5,7),(-2,-4,-5)] - CBSE (Science) Class 12 - Mathematics

ConceptElementary Operation (Transformation) of a Matrix

#### 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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Solution Using Elementary Row Transformations, Find the Inverse of the Matrix a = [(1,2,3),(2,5,7),(-2,-4,-5)] Concept: Elementary Operation (Transformation) of a Matrix.
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