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Question
If A = `[(2, -3),(5, -4),(-6, 1)], "B" = [(-1, 2),(2, 2), (0, 3)] and "C" = [(4, 3),(-1, 4),(-2, 1)]` Show that A + B = B + A
Solution
A + B = `[(2, -3),(5, -4),(-6, 1)] + [(-1, 2),(2, 2), (0, 3)]`
= `[(2 - 1, -3 + 2),(5 + 2, -4 + 2),(-6 + 0, 1 + 3)]`
∴ A + B = `[(1, -1),(7, -2),(-6, 4)]` ....(i)
B + A = `[(-1, 2),(2, 2), (0, 3)] + [(2, -3),(5, -4),(-6, 1)]`
= `[(-1 + 2, 2 - 3),(2 + 5, 2 - 4),(0 - 6, 3 + 1)]`
∴ B + A = `[(1, -1),(7, -2),(-6, 4)]` ....(ii)
From (i) and (ii), we get
A + B = B + A
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