Question

1. Show that the matrix A=\(\begin{bmatrix}1&-1&5\\-1&2&1\\5&1&3\end{bmatrix}\) is a symmetric matrix.
2. Show that the matrix A=\(\begin{bmatrix}0&1&-1\\-1&0&1\\1&-1&0\end{bmatrix}\) is a skew symmetric matrix

Answer 1

(i) We have: A'=\(\begin{bmatrix}1&-1&5\\-1&2&1\\5&1&3\end{bmatrix}\)=A so A'=A 

(i) We have: A'=\(\begin{bmatrix}0&-1&1\\1&0&-1\\-1&1&0\end{bmatrix}\)=-\(\begin{bmatrix}0&1&-1\\-1&0&1\\1&-1&0\end{bmatrix}\)=-A 

so A'=A Hence, A is a skew-symmetric matrix.