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Question
If A = `[(1, 2, -3),(-3, 7, -8),(0, -6, 1)], "B" = [(9, -1, 2),(-4, 2, 5),(4, 0, -3)]` then find the matrix C such that A + B + C is a zero matrix.
Solution
A + B + C is a zero martix.
∴ A + B + C = 0
∴ C = – (A + B)
= `- {[(1, 2, 3),(-3, 7, -8),(0, -6, 1)] + [(9, -1, 2),(-4, 2, 5),(4, 0, -3)]}`
= `-[(1 + 9, 2 - 1, -3 + 2),(-3 - 4, 7 + 2, -8 + 5),(0 + 4, -6 + 0, 1-3)]`
= `-[(10, 1, -1),(-7, 9, -3),(4, -6, -2)]`
= `[(-10, -1, 1),(7, -9, 3),(-4, 6, 2)]`
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