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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
Given, A' = `[(3,4),(-1,2),(0,1)]` and B = `[(-1,2,1),(1,2,3)]`
Then, A = `[(3, -1, 0),(4,2,1)]` and B' = `[(-1,1),(2,2),(1,3)]` [Because(A)' = A]
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)]`
`= [(2,1,1),(5,4,4)]`
Then, (A + B)' = `[(2,5),(1,4),(1,4)]` ....(i)
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)]`
`= [(2,5),(1,4),(1,4)]` ...(ii)
Equations (i) and (ii) prove that,
(A + B)' = A' + B'
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