Chapter 16.3, Problem 10WE

To determine

To find: the multiplication of the given two matrices.

Answer to Problem 10WE

  $\left[\begin{array}{ccc}0& 2& 0\\ -1& 1& 1\\ 1& 0& 0\end{array}\right]$.

Explanation of Solution

Given:

  $\left[\begin{array}{ccc}0& 2& 0\\ 0& 1& 1\\ 1& -1& 0\end{array}\right]\times \left[\begin{array}{ccc}1& 1& 0\\ 0& 1& 0\\ -1& 0& 1\end{array}\right]$ .

Concept used:

Two multiply the two matrices column of the first matrices must equals to the raw of the second matrices.

  $3\times 3$ matrices multiplication with its position is:.

Calculation:

  $\begin{array}{l}\left[\begin{array}{ccc}0& 2& 0\\ 0& 1& 1\\ 1& -1& 0\end{array}\right]\times \left[\begin{array}{ccc}1& 1& 0\\ 0& 1& 0\\ -1& 0& 1\end{array}\right]=\left[\begin{array}{ccc}0+0+0& 0+2+0& 0+0+0\\ 0+0-1& 0+1+0& 0+0+1\\ 1+0+0& 1-1+0& 0+0+0\end{array}\right].\\ \Rightarrow \left[\begin{array}{ccc}0& 2& 0\\ -1& 1& 1\\ 1& 0& 0\end{array}\right].\end{array}$

Hence, multiplication of matrices is $\left[\begin{array}{ccc}0& 2& 0\\ -1& 1& 1\\ 1& 0& 0\end{array}\right]$ .