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प्रश्न
If A = `[(2, 1),(-1, 3)], B = [(-3, 2),(4, 1)], C = [(-3, 0),(4, 1)]`, verify the following:
(A + B) + C = A + (B + C)
योग
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उत्तर
Find A + B
A + B = `[(2 + (-3), 1 + 2),(-1 + 4, 3 + 1)]`
= `[(-1, 3),(3, 4)]`
Find (A + B) + C
(A + B) + C = `[(-1, 3),(3, 4)] + [(-3, 0),(4, 1)]`
= `[(-1 + (-3), 3 + 0),(3 + 4, 4 + 1)]`
= `[(-4, 3),(7, 5)]`
Find B + C
B + C = `[(-3 + (-3), 2 + 0),(4 + 4, 1 + 1)]`
= `[(-6, 2),(8, 2)]`
Find A + (B + C)
A + (B + C) = `[(2, 1),(-1, 3)] + [(-6, 2),(8, 2)]`
= `[(2 + (-6), 1 + 2),(-1 + 8, 3 + 2)]`
= `[(-4, 3),(7, 5)]`
(A + B) + C = `[(-4, 3),(7, 5)]`
A + (B + C) = `[(-4, 3),(7, 5)]`
Hence Verified,
(A + B) + C = A + (B + C)
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