For each of the following matrices, find its transpose and state whether it is symmetric, skew- symmetric or neither. [251-546-1-63]

Exercise 2.2 | Q 9.2 | Page 47

QUESTION

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

${\displaystyle \left[\begin{array}{ccc}2& 5& 1\\ -5& 4& 6\\ -1& -6& 3\end{array}\right]}$

${\displaystyle }$

SOLUTION

Let A = ${\displaystyle \left[\begin{array}{ccc}2& 5& 1\\ -5& 4& 6\\ -1& -6& 3\end{array}\right]}$

∴ A^T = ${\displaystyle \left[\begin{array}{ccc}2& -5& -1\\ -5& 4& -6\\ 1& 6& 3\end{array}\right]}$

∴ A^T = ${\displaystyle \left[\begin{array}{ccc}-2& 5& 1\\ -5& -4& 6\\ -1& -6& -3\end{array}\right]}$

∴ A ≠ A^T and A ≠ – A^T
∴ A is neither symmetric nor skew – symmetric matrix.