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Question
If A = `[(1, -2),(3, -5),(-6, 0)],"B" = [(-1, -2),(4, 2),(1, 5)] "and C" = [(2, 4),(-1, -4),(-3, 6)]`, find the matrix X such that 3A – 4B + 5X = C.
Solution
3A – 4B + 5X = C
∴ 5X = C + 4B – 3A
= `[(2, 4),(-1, -4),(-3, 6)] + 4[(-1, -2),(4, 2),(1, 5)] - 3[(1, -2),(3, -5),(-6, 0)]`
= `[(2, 4),(-1, -4),(-3, 6)] + [(-4, -8),(16, 8),(4, 20)] - [(3, -6),(9, -15),(-18, 0)]`
= `[(2 - 4 - 3, 4 - 8 + 6),(-1 + 16 - 9, -4 + 8 + 15),(-3 + 4 + 18, 6 + 20 - 0)]`
= 5X = `[(-5, 2),(6, 19),(19, 26)]`
∴ X = `(1)/(5) [(-5, 2),(6, 19),(19, 26)]`
= `[(-1,2/5),(6/5, 19/5), (19/5, 26/5)]`
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