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Question
Find the inverse of the following matrix (if they exist):
`((1,3),(2,7))`
Solution
Let A = `[(1,3),(2,7)]`
∴ |A| = `|(1,3),(2,7)|` = 7 - 6 = 1 ≠ 0
∴ A-1 exists.
Consider AA-1 = I
∴ `[(1,3),(2,7)] "A"^-1 = [(1,0),(0,1)]`
By R2 - 2R1, we get,
`[(1,3),(0,1)] "A"^-1 = [(1,0),(-2,1)]`
By R1 - 3R2 we get,
`[(1,0),(0,1)] "A"^-1 = [(7,-3),(-2,1)]`
A-1 = `[(7,-3),(-2,1)]`
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