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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
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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