Question

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

Answer 1

$\left[\begin{array}{ccc}2& 1& 3\end{array}\right]\left[\begin{array}{ccc}-1& 0& -1\\ -1& 1& 0\\ 0& 1& 1\end{array}\right]\left[\begin{array}{c}1\\ 0\\ -1\end{array}\right]=A$

Order of A

$\Rightarrow \left[\begin{array}{ccc}-2-1+0& 0+1+3& -2+0+3\end{array}\right]\left[\begin{array}{c}1\\ 0\\ -1\end{array}\right]$

$\Rightarrow \left[\begin{array}{ccc}-3& 4& 1\end{array}\right]\left[\begin{array}{c}1\\ 0\\ -1\end{array}\right]$

$\Rightarrow \left[\begin{array}{ccc}-3& +0& -\end{array}\right]=\left[-4\right]$

Order of A is (1 x 1)