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Question
Answer the following question:
Find matrices A and B, where 3A – B = `[(-1, 2, 1),(1, 0, 5)]` and A + 5B = `[(0, 0, 1),(-1, 0, 0)]`
Solution
Given equations are
3A – B = `[(-1, 2, 1),(1, 0, 5)]` ...(i)
and A + 5B = `[(0, 0, 1),(-1,0, 0)]` ...(ii)
By (i) × 5 + (ii), we get
16A = `5[(-1, 2, 1),(1, 0, 5)] + [(0, 0, 1),(-1, 0, 0)]`
= `[(-5, 10, 5),(5, 0, 25)] + [(0, 0, 1),(-1, 0, 0)]`
∴ 16A = `[(-5, 10, 6),(4, 0, 25)]`
∴A = `1/16[(-5, 10, 6),(4, 0, 25)]`
By (i) – (ii) × 3, we get
–16B = `[(-1, 2, 1),(1, 0, 5)] -3[(0, 0, 1),(-1, 0, 0)]`
= `[(-1, 2, 1),(1, 0, 5)] - [(0, 0, 3),(-3, 0, 0)]`
∴ –16B = `[(-1, 2, -2),(4, 0, 5)]`
∴ B = `(-1)/16 [(-1, 2, -2),(4, 0, 5)]`
∴ B = `1/16 [(1, -2, 2),(-4, 0, -5)]`
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