Question

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

`[(0, 1 + 2"i", "i" - 2),(-1 - 2"i", 0, -7),(2 - "i", 7, 0)]`

Answer 1

Let A = `[(0, 1 + 2"i", "i" - 2),(-1 - 2"i", 0, -7),(2 - "i", 7, 0)]`

∴ A^T = `[(0, -1 - 2"i", 2 - "i"),(1 + 2"i", 0, 7),("i" - 2, -7, 0)]`

∴ A^T = `[(0, 1 + 2"i", "i" - 2),(-1 - 2"i", 0, -7),(2 - "i", 7, 0)]`

^∴ A^T = – A i.e. A = – A^T

∴ A is a skew-symmetric matrix.