Chapter 16.2, Problem 1WE

To determine

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

Answer to Problem 1WE

The solution for $X$ is $\left[\begin{array}{cc}6& -4\\ 10& 1\end{array}\right]$ .

Explanation of Solution

Given information:

Given equation,

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

Calculation: Consider the givn equation,

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

Now, solve the equation as shown,

  $\begin{array}{c}X-\left[\begin{array}{cc}0& 5\\ 1& -2\end{array}\right]=3\left[\begin{array}{cc}2& -3\\ 3& 1\end{array}\right]\\ X=3\left[\begin{array}{cc}2& -3\\ 3& 1\end{array}\right]+\left[\begin{array}{cc}0& 5\\ 1& -2\end{array}\right]\\ X=\left[\begin{array}{cc}3\cdot 2& 3\cdot \left(-3\right)\\ 3\cdot 3& 3\cdot 1\end{array}\right]+\left[\begin{array}{cc}0& 5\\ 1& -2\end{array}\right]\\ X=\left[\begin{array}{cc}6& -9\\ 9& 3\end{array}\right]+\left[\begin{array}{cc}0& 5\\ 1& -2\end{array}\right]\\ X=\left[\begin{array}{cc}6+0& -9+5\\ 9+1& 3+\left(-2\right)\end{array}\right]\\ X=\left[\begin{array}{cc}6& -4\\ 10& 1\end{array}\right]\end{array}$

Hence the solution for $X$ is $\left[\begin{array}{cc}6& -4\\ 10& 1\end{array}\right]$ .