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Question
Find the inverse of the following matrix (if they exist):
`[(3,-10),(2,-7)]`
Solution
Let A = `[(3,-10),(2,-7)]`
∴ |A| = `|(3,-10),(2,-7)| = - 21 + 20 = - 1 ne 0`
∴ A-1 exists.
Consider AA-1 = I
∴ `[(3,-10),(2,-7)] "A"^-1 = [(1,0),(0,1)]`
By R1 - R2, we get,
∴ `[(1,-3),(2,-7)] "A"^-1 = [(1,-1),(0,1)]`
By R2 - 2R1, we get,
`[(1,-3),(0,-1)] "A"^-1 = [(1,-1),(-2,3)]`
By (- 1)R2, we get,
`[(1,-3),(0,1)] "A"^-1 = [(1,-1),(2,-3)]`
By R1 + 3R2, we get,
`[(1,0),(0,1)] "A"^-1 = [(7,-10),(2,-3)]`
∴ `"A"^-1 = [(7,-10),(2,-3)]`
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