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