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Question
if `A = [(-1,2,3),(5,7,9),(-2,1,1)] and B = [(-4,1,-5),(1,2,0),(1,3,1)]` then verify that (A- B)' = A' - B'
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Solution
Given, `"A" = [(-1,2,3),(5,7,9),(-2,1,1)]` and B = `[(-4,1,-5),(1,2,0),(1,3,1)]`
Then, (A - B) = `"A" = [(-1,2,3),(5,7,9),(-2,1,1)] - [(-4,1,-5),(1,2,0),(1,3,1)]`
`= [(-1 + 4, 2 - 1, 3 + 5),(5 - 1, 7 - 2, 9 - 0), (-2 - 1, 1 - 3, 1 - 1)] = [(3,1,8),(4,5,9),(-3, -2, 0)]`
Then, (A - B)' = `[(3,1,8),(4,5,9),(-3, -2, 0)] = [(3,4,-3),(1,5,-2),(8, 9, 0)] ` ...(i)
We know that, A' = `[(-1, 5, -2), (2, 7,1),(3, 9,1)]` तथा B' = `[(-4,1,1),(1,2,3),(-5,0,1)]`
A' - B' = `[(-1, 5, -2), (2, 7,1),(3, 9,1)] - [(-4,1,1),(1,2,3),(-5,0,1)]`
`= [(-1 + 4, 5 - 1, -2 - 1),(2 - 1, 7 - 2, 1 - 3),(3 + 5, 9 - 0, 1 - 1)]`
`= [(3,4,-3),(1,5,-2),(8,9,0)]` ... (ii)
Equations (i) and (ii) prove that,
(A - B)' = A' - B'
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