Chapter 16.2, Problem 17WE

To determine

To solve: the given equation for matrix $X$ .

Answer to Problem 17WE

The solution for $X$ is $\left[\begin{array}{cc}2& -4\\ -10& 3\end{array}\right]$ .

Explanation of Solution

Given information:

Given equation,

  $X+\left[\begin{array}{cc}0& 4\\ 9& -1\end{array}\right]=\left[\begin{array}{cc}2& 0\\ -1& 2\end{array}\right]$

Calculation: Consider the givn equation,

  $X+\left[\begin{array}{cc}0& 4\\ 9& -1\end{array}\right]=\left[\begin{array}{cc}2& 0\\ -1& 2\end{array}\right]$

Now, solve the equation as shown,

  $\begin{array}{c}X+\left[\begin{array}{cc}0& 4\\ 9& -1\end{array}\right]=\left[\begin{array}{cc}2& 0\\ -1& 2\end{array}\right]\\ X=\left[\begin{array}{cc}2& 0\\ -1& 2\end{array}\right]-\left[\begin{array}{cc}0& 4\\ 9& -1\end{array}\right]\\ X=\left[\begin{array}{cc}2-0& 0-4\\ -1-9& 2-\left(-1\right)\end{array}\right]\\ X=\left[\begin{array}{cc}2& -4\\ -10& 3\end{array}\right]\end{array}$

Hence the solution for $X$ is $\left[\begin{array}{cc}2& -4\\ -10& 3\end{array}\right]$ .