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Question
Find inverse of the following matrices (if they exist) by elementary transformations :
`[(1, -1),(2, 3)]`
Solution
Let A = `[(1, -1),(2, 3)]`
∴ |A| = `|(1, -1),(2, 3)|`
= 3 + 2
= 5 ≠ 0
∴ A–1 exists.
Consider AA–1 = I
∴ `[(1, -1),(2, 3)] "A"^-1 = [(1, 0),(0, 1)]`
Applying R2 → R2 – 2R1, we get
`[(1, -1),(0, 5)] "A"^-1 = [(1, 0),(-2, 1)]`
Applying R2 → `(1/5)` R2, we get
`[(1, -1),(0, 1)] "A"^-1 = [(1, 0),(-2/5, 1/5)]`
Applying R1 → R1 – R2, we get
`[(1, 0),(0, 1)] "A"^-1 = [(3/5, 1/5),(-2/5, 1/5)]`
∴ A–1 = `[(3/5, 1/5),(-2/5, 1/5)]`.
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