Chapter 16.1, Problem 15WE

To determine

To find: the value of given variable.

Answer to Problem 15WE

  $x=3,y=-4,z=-4$ .

Explanation of Solution

Given information:

Given symbol,

  $\left[\begin{array}{cc}8-y& 0\\ x+2z& x+z\end{array}\right]=\left[\begin{array}{cc}-3y& 0\\ -5& -1\end{array}\right]$

Calculation: Now, $\left[\begin{array}{cc}8-y& 0\\ x+2z& x+z\end{array}\right]=\left[\begin{array}{cc}-3y& 0\\ -5& -1\end{array}\right]$

Since the matrices are equal elements in corresponding positions are equal.

Therefore, $8-y=-3y$ and $x+2z=-5$ and $x+z=-1$

Now,

  $\begin{array}{c}8-y=-3y\\ 8=y-3y\\ 8=-2y\\ 4=-y\\ y=-4\end{array}$

Now $x+2z=-5$ and $x+z=-1$

  $\begin{array}{l}\underset{\_}{\begin{array}{l}x+2z=-5\\ x+z=-1\end{array}}\\ z=-4\end{array}$

Since,

  $\begin{array}{c}x+z=-1\\ x+\left(-4\right)=-1\\ x=-1+4\\ x=3\end{array}$

Thus, $x=3,y=-4,z=-4$