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प्रश्न
If `A = [(1, 2, -3),(5, 0, 2),(1, -1, 1)], B = [(3, -1, 2),(4, 2, 5),(2, 0, 3)] and C = [(4, 1, 2),(0, 3, 2),(1, -2, 3)]` then compute (A + B) and (B – C). Also verify that A + (B – C) = (A + B) – C.
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उत्तर
`A + B = [(1, 2, -3),(5, 0, 2),(1, -1, 1)] + [(3, -1, 2),(4, 2, 5),(2, 0, 3)]`
= `[(1 + 3, 2 - 1, -3 + 2),(5 + 4, 0 + 2, 2 + 5),(1 + 2, -1 + 0, 1 + 3)]`
= `[(4, 1, -1),(9, 2, 7),(3, -1, 4)]`
`B - C = [(3, -1, 2),(4, 2, 5),(2, 0, 3)] - [(4, 1, 2),(0, 3, 2),(1, -2, 3)]`
= `[(3 - 4, -1 - 1, 2 - 2),(4 - 0, 2 - 3, 5 - 2),(2 - 1, 0 - (-2), 3 - 3)]`
= `[(-1, -2, 0),(4, -1, 3),(1, 2, 0)]`
`A + (B - C) = [(1, 2, -3),(5, 0, 2),(1, -1, 1)] + [(-1, -2, 0),(4, -1, 3),(1, 2, 0)]`
= `[(1 + (-1), 2 + (-2), -3 + 0),(5 + 4, 0 + (-1), 2 + 3), (1 + 1, -1 + 2, 1 + 0)]`
= `[(0, 0, -3),(9, -1, 5),(2, 1, 1)]`
`(A + B) - C = [(4, 1, -1),(9, 2, 7),(3, -1, 4)] - [(4, 1, 2),(0, 3, 2),(1, -2, 3)]`
= `[(4 - 4, 1 - 1, -1 - 2),(9 - 0, 2 - 3, 7 - 2),(3 - 1, -1 - (-2), 4 - 3)]`
= `[(0, 0, -3),(9, -1, 5),(2, 1, 1)]`
Hence, we verified that A + (B – C) = (A + B) – C.
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