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Question
Answer the following question:
if A = `[(-3, 2),(2, -4)]`, B = `[(1, x),(y, 0)]`, and (A + B)(A – B) = A2 – B2 , find x and y
Solution
(A + B)(A – B) = A2 – B2
∴ A2 – AB + BA – B2 = A2 – B2
∴ –AB + BA = 0
∴ AB = BA
∴ `[(-3, 2),(2, -4)] [(1, x),(y, 0)] = [(1, x),(y, 0)] [(-3, 2),(2, -4)]`
∴ `[(-3 + 2y, -3x +0),(2 - 4y, 2x + 0)] = [(-3 + 2x, 2 - 4x),(-3y + 0, 2y + 0)]`
∴ By equality of matrices, we get
2 – 4x = – 3x
∴ x = 2
and 2y = 2x
∴ y = x
∴ y = 2
∴ x = 2, y = 2
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