Chapter 2.3, Problem 7CFU

To determine

To find: value of $x\text{ and }y$ for the given matrix equation.

Answer to Problem 7CFU

  $\begin{array}{l}x=4\\ y=0\end{array}$

Explanation of Solution

Given information:

The given matrix equation is as follows:

  $\left[\begin{array}{ccc}16& 0& 2x\end{array}\right]=\left[\begin{array}{ccc}4x& y& 8-y\end{array}\right]$

Calculation:

Since the corresponding elements are equal, so the equality of the

Matrices can be represented as follows:

  $\begin{array}{l}16=4x\mathrm{...}\left(1\right)\\ 0=y\mathrm{...}\left(2\right)\\ 2x=8-y\mathrm{...}\left(3\right)\end{array}$

Equation (2) shows that $y=0$

Solve equation (1) as follows:

  $\begin{array}{c}16=4x\\ x=\frac{16}{4}\\ =4\end{array}$

Thus, the values of x and y are 4 and 0 respectively.