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Question
Find the matrix X such that AX = I where A = `[(6, 17),(1, 3)]`
Solution
Given, AX = I
∴ `[(6, 17),(1, 3)]` X = `[(1, 0),(0, 1)]`
Applying R1 ↔ R2, we get
`[(1, 3),(6, 17)]` X = `[(0, 1),(1, 0)]`
Applying R2 → R2 – 6R1, we get
`[(1, 3),(0, -1)]` X = `[(0, 1),(1, -6)]`
Applying R1 → R1 + 3R2, we get
`[(1, 0),(0, -1)]` X = `[(3, -17),(1, -6)]`
Applying R2 → (–1) R2, we get
`[(1, 0),(0, 1)]` X = `[(3, -17),(-1, 6)]`
∴ X = `[(3, -17),(-1, 6)]`
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