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Question
For each of the following matrices, find its transpose and state whether it is symmetric, skew-symmetric, or neither.
`[(2, 5, 1),(-5, 4, 6),(-1, -6, 3)]`
Solution
Let A = `[(2, 5, 1),(-5, 4, 6),(-1, -6, 3)]`
∴ AT = `[(2, -5, -1),(5, 4, -6),(1, 6, 3)]`
∴ –AT = `[(-2, 5, 1),(-5, -4, 6),(-1, -6, -3)]`
∵ A ≠ AT and A ≠ –AT
∴ A is neither a symmetric nor a skew-symmetric matrix.
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