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Question
Find the inverse of the following matrices by transformation method: `[(1, 2),(2, -1)]`
Solution
Let A = `[(1, 2),(2, -1)]`
∴ |A| = `|(1, 2),(2, -1)|` = – 1 – 4 = –5 ≠ 0
∴ A–1 exists.
Consider AA–1 = I
∴ `[(1, 2),(2, -1)]"A"^-1 = [(1, 0),(0, 1)]`
Appying R2 → R2 – 2R1, we get
`[(1, 2),(0, -5)]"A"^-1 = [(1, 0),(-2, 1)]`
Applying R2 → `(-1/5)`R2, we get
`[(1, 2),(0, 1)]"A"^-1 = [(1, 0),(2/5, (-1)/5)]`
Appying R1 → R1 – 2R2, we get
`[(1, 0),(0, 1)]"A"^-1 = [(1/5, 2/5),(2/5, -1/5)]`
∴ A–1 = `(1)/(5)[(1, 2),(2, -1)]`
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