Chapter 2.3, Problem 18E

To determine

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

Answer to Problem 18E

  $\begin{array}{l}x=4\\ y=2\end{array}$

Explanation of Solution

Given information:

The given matrix equation is as follows:

  $\left[\begin{array}{cc}x& y\end{array}\right]=\left[\begin{array}{cc}2y& 2x-6\end{array}\right]$

Calculation:

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

Matrices can be represented as follows:

  $\begin{array}{l}x=2y\mathrm{...}\left(1\right)\\ y=2x-6\mathrm{...}\left(2\right)\end{array}$

Put the value of x in equation (2) and solve as follows:

  $\begin{array}{c}y=2\left(2y\right)-6\\ y=4y-6\\ y-4y=-6\\ -3y=-6\\ y=\frac{-6}{-3}\\ =2\end{array}$

Put the value of y in equation (1) and solve as follows:

  $\begin{array}{c}x=2\left(2\right)\\ =4\end{array}$

Thus, the values of x and y are 4 and 2 respectively.