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Question
if `A' [(3,4),(-1, 2),(0,1)] and B = [((-1,2,1),(1,2,3))]` then verify that (A - B)' = A' - B'
Solution
We know that, `"A" = [(3, -1, 0),(4,2,1)]` and B' = `[(-1,1),(2,2),(1,3)]`
Now, (A - B) = `[(3, -1, 0),(4,2,1)] - [(-1,2,1),(1,2,3)]`
`= [(3 + 1, -1 -2, 0 - 1),(4 - 1, 2 - 2, 1 - 3)]`
`= [(4, -3,-1),(3, 0,-2)]`
so, (A - B)' = `[(4,3),(-3,0),(-1,-2)]` ..... (i)
Then, A' - B' = `[(3,4),(-1,2),(0,1)] - [(-1,1),(2,2),(1,3)]`
`= [(3 + 1, 4 - 1),(-1 - 2, 2 - 2), (0 - 1, 1 - 3)]`
`= [(4,3),(-3,0),(-1,-2)]` ..... (ii)
Equations (i) and (ii) prove that,
(A - B)' = A' - B'
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