Chapter 4.2, Problem 39HP

To determine

To find: The example for matrix A and B for the given condition.

Answer to Problem 39HP

The matrix $A=\left[\begin{array}{cc}6& 1\\ 6& 3\end{array}\right]$ and $B=\left[\begin{array}{cc}3& 2\\ 4& 2\end{array}\right]$ .

Explanation of Solution

Given:

The given equation for matrix is $4D-3C$ .

Calculation:

Consider the given matrix equation is,

  $4B-3A=\left[\begin{array}{cc}-6& 5\\ -2& -1\end{array}\right]$

Consider the matrix $A$ is,

  $A=\left[\begin{array}{cc}6& 1\\ 6& 3\end{array}\right]$

Consider the matrix $B$ is,

  $B=\left[\begin{array}{cc}3& 2\\ 4& 2\end{array}\right]$

Then,

  $\begin{array}{c}4\left[\begin{array}{cc}3& 2\\ 4& 2\end{array}\right]-3\left[\begin{array}{cc}6& 1\\ 6& 3\end{array}\right]=\left[\begin{array}{cc}12& 8\\ 16& 8\end{array}\right]-3\left[\begin{array}{cc}8& 3\\ 6& 3\end{array}\right]\\ =\left[\begin{array}{cc}12-18& 8-3\\ 16-18& 8-9\end{array}\right]\\ =\left[\begin{array}{cc}-6& 5\\ -2& -1\end{array}\right]\end{array}$