Chapter 16.4, Problem 2ST

To determine

To find: the value of given variable.

Answer to Problem 2ST

The values are $x=2,y=-10,z=2$ .

Explanation of Solution

Given information:

Given variable,

  $\left[\begin{array}{c}3x+2\\ 10\\ 0\end{array}\right]=\left[\begin{array}{c}8\\ -y\\ z-4\end{array}\right]$

Calculation:

Two matrices of same order are equal if their corresponding elements are equal.

Therefore,

  $\left[\begin{array}{c}3x+2\\ 10\\ 0\end{array}\right]=\left[\begin{array}{c}8\\ -y\\ z-4\end{array}\right]$

If two matrices have the same dimensions and the elements in all corresponding positions are equal, then the matrices are equal.

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

  $\begin{array}{l}3x+2=8-y=10z-2=0\\ 3x=6y=-10z=2\\ x=2y=-10z=2\end{array}$

Therefore, the values are $x=2,y=-10,z=2$ .