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Question
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.
Solution
`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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