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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'
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)]`
`= [(-5, 3, -2),(6, 9,9),(-1,4,2)]`
Now, (A + B)' `= [(-5,6,-1),(3,9,4),(-2,9,2)]` ...(i)
A' = `[(-1,5,-2),(2,7,1),(3,9,1)]` and B' = `[(-4,1,1),(1,2,3),(-5,0,1)]`
then, 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)]`
`[(-5,6,-1),(3,9,4),(-2,9,2)]` ...(ii)
Equations (i) and (ii) prove that,
(A + B)' = A' + B'
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