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Question
Find A−1 using column transformations:
A = `[(5, 3),(3, -2)]`
Solution
We know that A−1 = I
∴ `[(5, 3),(3, -2)]` A−1 = `[(1, 0),(0, 1)]`
Applying C1 → 2C2 – C1, we get
`[(1, 3),(-7, -2)]` A−1 = `[(-1, 0),(2, 1)]`
Applying C2 → C2 – 3C1, we get
`[(1, 0),(-7, 19)]` A−1 = `[(-1, 3),(2, -5)]`
Applying C2 → `(1/19)` C2, we get
`[(1, 0),(-7, 1)]` A−1 = `[(-1, 3/19),(2, (-5)/19)]`
Applying C1 → C1 + 7C2, we get
`[(1, 0),(0, 1)]` A−1 = `[(2/19, 3/19),(3/19, (-5)/19)]`
∴ A−1 = `1/19 [(2, 3),(3, -5)]`
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