Chapter 11, Problem 8CT

To determine

To find: The matrix $A-3C$ .

Answer to Problem 8CT

The matrix $A-3C$ is $\left[\begin{array}{cc}-11& -19\\ -3& 5\\ 6& -22\end{array}\right]$ .

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

  $A-3C$

Substitute the values in the above relation.

  $\begin{array}{c}A-3C=\left[\begin{array}{cc}1& -1\\ 0& -4\\ 3& 2\end{array}\right]-3\left[\begin{array}{cc}4& 6\\ 1& -3\\ -1& 8\end{array}\right]\\ =\left[\begin{array}{cc}1& -1\\ 0& -4\\ 3& 2\end{array}\right]-\left[\begin{array}{cc}12& 18\\ 3& -9\\ -3& 24\end{array}\right]\\ =\left[\begin{array}{cc}-11& -19\\ -3& 5\\ 6& -22\end{array}\right]\end{array}$

Therefore, the matrix $A-3C$ is $\left[\begin{array}{cc}-11& -19\\ -3& 5\\ 6& -22\end{array}\right]$ .