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Question
Answer the following question:
Find matrices A and B, where 2A – B = `[(1, -1),(0, 1)]` and A + 3B = `[(1, -1),(0, 1)]`
Solution
Given equations are
2A – B = `[(1, -1),(0, 1)]` ....(i)
and A + 3B = `[(1, -1),(0, 1)]` ...(ii)
By (i) × 3 + (ii), we get
7A = `3[(1, -1),(0, 1)] + [(1, -1),(0, 1)]`
∴ 7A = `[(3, -3),(0, 3)] + [(1, -1),(0, 1)]`
∴ 7A = `[(4, -4),(0, 4)]`
∴ A = `1/7[(4, -4),(0, 4)]`
By (i) – (ii) × 2, we get
–7B = `[(1, -1),(0, 1)] -2[(1, -1),(0, 1)]`
= `[(1, -1),(0, 1)] - [(2, -2),(0, 2)]`
∴ –7B = `[(-1, 1),(0, -1)]`
∴ B = `- 1/7[(-1, 1),(0, -1)]`
∴ B = `1/7[(1, -1),(0, 1)]`
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