Question

For each of the following matrices, find its transpose and state whether it is symmetric, skew- symmetric or neither.

`[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`

Answer 1

Let A = `[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`

∴ A^T = `[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`

∴ A^T = A i.e., A = A^T
∴ A is a symmetric matrix.