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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'
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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)]` ...[∵ (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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