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Question
Find `1/2` (A + A') and `1/2` (A – A'), when A = `[(0, a, b),(-a, 0, c),(-b, -c, 0)]`
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Solution
Given A = `[(0, a, b),(-a, 0, c),(-b, -c, 0)]`
So, A' = `[(0, -a, -b),(a, 0, -c),(b, c, 0)] = -[(0, a, b),(-a, 0, c),(-b, -c, 0)]` = –A
Now, `1/2` (A + A') = `1/2 ([(0, a, b),(-a, 0, c),(-b, -c, 0)] - [(0, a, b),(-a, 0, c),(-b, -c, 0)])`
= `[(0, 0, 0),(0, 0, 0),(0, 0, 0)]`
Then, `1/2` (A – A') = `1/2 ([(0, a, b),(-a, 0, c),(-b, -c, 0)] + [(0, a, b),(-a, 0, c),(-b, -c, 0)])`
= `1/2 [(0, 2a, 2b),(-2a, 0, 2c),(-2b, -2c, 0)]`
= `[(0, a, b),(-a, 0, c),(-b, -c, 0)]`
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