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)]`

Answer 1

Let A = `[(2, 5, 1),(-5, 4, 6),(-1, -6, 3)]`

∴ A^T = `[(2, -5, -1),(5, 4, -6),(1, 6, 3)]`

∴ –A^T = `[(-2, 5, 1),(-5, -4, 6),(-1, -6, -3)]`

∵ A ≠ A^T and A ≠ –A^T

∴ A is neither a symmetric nor a skew-symmetric matrix.