Chapter 8, Problem 45RE

To determine

The value of the X using the given matrix.

Explanation of Solution

Given:

The matrices are given as:

  $A=\left[\begin{array}{l}-40\\ 1-5\\ -32\end{array}\right],B=\left[\begin{array}{l}12\\ -21\\ 44\end{array}\right]$

And the equation is:

  $X=2A-3B$

Solving the given equation:

  $\begin{array}{l}X=2A-3B\\ =2\left[\begin{array}{l}-40\\ 1-5\\ -32\end{array}\right]-3\left[\begin{array}{l}12\\ -21\\ 44\end{array}\right]\\ =\left[\begin{array}{l}-8-30-6\\ 2-\left(-6\right)-10-3\\ -6-124-12\end{array}\right]\\ =\left[\begin{array}{c}-11-6\\ 8-13\\ -18-8\end{array}\right]\end{array}$

Therefore, the value of the X:

  $\left[\begin{array}{c}-11-6\\ 8-13\\ -18-8\end{array}\right]$