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प्रश्न
For the matrix A = `[(1,5),(6,7)]` verify that (A + A') is a symmetric matrix.
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उत्तर
Given, A = `[(1,5),(6,7)]`
So, A' = `[(1,6),(5,7)]`
Now, (A + A') = `[(1,5),(6,7)] + [(1,6),(5,7)]`
`= [(1 +1, 5 +6), (6 + 5, 7 + 7)]`
`= [(2, 11),(11, 14)]`
Then, (A + A')' = `[(2, 11),(11, 14)]`
∵ (A + A')' = (A + A'),
Hence it is proved that the matrix (A + A')' is a symmetric matrix.
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