Chapter 11, Problem 10CT

To determine

To find: The matrix $BA$ .

Answer to Problem 10CT

The matrix $BA$ is $\left[\begin{array}{cc}16& 17\\ 3& -10\end{array}\right]$ .

Explanation of Solution

Given information:

The matrix A is

  $A=\left[\begin{array}{cc}1& -1\\ 0& -4\\ 3& 2\end{array}\right]$

The matrix B is

  $B=\left[\begin{array}{ccc}1& -2& 5\\ 0& 3& 1\end{array}\right]$

The matrix C is

  $C=\left[\begin{array}{cc}4& 6\\ 1& -3\\ -1& 8\end{array}\right]$

Calculation:

The relation between the matrices is

  $BA$

Substitute the values in the above relation.

  $\begin{array}{c}BA=\left[\begin{array}{ccc}1& -2& 5\\ 0& 3& 1\end{array}\right]\left[\begin{array}{cc}1& -1\\ 0& -4\\ 3& 2\end{array}\right]\\ =\left[\begin{array}{cc}1\times 1+\left(-2\right)\times 0+5\times 3& 1\times \left(-1\right)+\left(-2\right)\times \left(-4\right)+5\times 2\\ 0\times 1+\left(3\right)\times 0+1\times 3& 0\times \left(-1\right)+\left(3\right)\times \left(-4\right)+1\times 2\end{array}\right]\\ =\left[\begin{array}{cc}16& 17\\ 3& -10\end{array}\right]\end{array}$

Therefore, the matrix $BA$ is $\left[\begin{array}{cc}16& 17\\ 3& -10\end{array}\right]$ .