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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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