Question

If $\left[\begin{array}{ccc}2& 1& 3\end{array}\right]\left(\begin{array}{ccc}-1& 0& -1\\ -1& 1& 0\\ 0& 1& 1\end{array}\right)\left(\begin{array}{c}1\\ 0\\ -1\end{array}\right)=\mathrm{A}$, then write the order of matrix A.

Answer 1

Consider, $\left(213\right)\left(\begin{array}{ccc}-1& 0& -1\\ -1& 1& 0\\ 0& 1& 1\end{array}\right)\left(\begin{array}{c}1\\ 0\\ -1\end{array}\right)=\mathrm{A}$
Order of matrix $\left(213\right)$ is 1 × 3.
Order of matrix$\left(\begin{array}{ccc}-1& 0& -1\\ -1& 1& 0\\ 0& 1& 1\end{array}\right)$ is 3 × 3
Order of matrix$\left(\begin{array}{c}1\\ 0\\ -1\end{array}\right)$ is 3 × 1
Therefore, order of $\left(213\right)\left(\begin{array}{ccc}-1& 0& -1\\ -1& 1& 0\\ 0& 1& 1\end{array}\right)\left(\begin{array}{c}1\\ 0\\ -1\end{array}\right)$ is 1 × 1.