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Question
If possible, using elementary row transformations, find the inverse of the following matrices
`[(2, 3, -3),(-1, 2, 2),(1, 1, -1)]`
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Solution
Here, A = `[(2, 3, -3),(-1, 2, 2),(1, 1, -1)]`
Put A = IA
`[(2, 3, -3),(-1, 2, 2),(1, 1, -1)] = [(1, 0, 0),(0, 1, 0),(0, 0, 1)]"A"`
R1 → R1 – 2R3 and R2 → R2 + R1
`[(0, 1, -1),(0, -1, 1),(1, 1, -1)] = [(1, 0, -2),(0, 1, 1),(0, 0, 1)]"A"`
R1 → R1 + R2
`[(0, 0, 0),(0, -1, 1),(1, 1, -1)] = [(1, 1, -1),(0, 1, 1),(0, 0, 1)]"A"`
First row on L.H.S. contains all zeros
So the inverse of the given matrix A does not exist.
Hence, matrix A has no inverse.
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