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Question
Find inverse of the following matrices (if they exist) by elementary transformations :
`[(2, 1),(7, 4)]`
Solution
Let A = `[(2, 1),(7, 4)]`
∴ |A| = `|(2, 1),(7, 4)|`
= 8 – 7
= 1 ≠ 0
∴ A–1 exists.
Consider AA–1 = I
∴ `[(2, 1),(7, 4)] "A"^-1 = [(1, 0),(0, 1)]`
Applying R1 → 4R1 – R2, we get
`[(1, 0),(7, 4)] "A"^-1 = [(4, -1),(0, 1)]`
Applying R2 → R2 – 7R1, we get
`[(1, 0),(0, 1)] "A"^-1 = [(4, -1),(-7, 2)]`
Applying R2 → `(1/4)` R2, we get
`[(1, 0),(0, 1)] "A"^-1 = [(4, -1),(-7, 2)]`
∴ A–1 = `[(4, -1),(-7, 2)]`.
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