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Question
Find the inverse of the matrices (if it exists).
`[(-1,5),(-3,2)]`
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Solution
A = `[(-1,5),(-3,2)]`
|A| = `|(-1,5),(-3,2)|`
= −2 + 15
= 13 ≠ 0
Therefore, A−1 exists.
A11 = (−1)1+1 (2) = 2
A12 = (−1)1+2 (−3) = 3
A21 = (−1)2+1 (5) = −5
A22 = (−1)2+2 (−1) = −1
∴ Adj A = `[(2,3),(-5,-1)] = [(2,-5),(3,-1)]`
A−1 = `1/|A|` (adj A)
= `1/13 [(2,-5),(3,-1)]`
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