Chapter 2.3, Problem 5CFU

To determine

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

Answer to Problem 5CFU

  $\begin{array}{l}x=7\\ y=2\end{array}$

Explanation of Solution

Given information:

The given matrix equation is as follows:

  $\left[\begin{array}{c}2y\\ x\end{array}\right]=\left[\begin{array}{c}x-3\\ y+5\end{array}\right]$

Calculation:

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

Matrices can be represented as follows:

  $\begin{array}{l}2y=x-3\mathrm{...}\left(1\right)\\ x=y+5\mathrm{...}\left(2\right)\end{array}$

Now, substitute value of x in equation (1) and solve as follows:

  $\begin{array}{c}2y=\left(y+5\right)-3\\ 2y=y+2\\ 2y-y=2\\ y=2\end{array}$

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

  $\begin{array}{c}x=2+5\\ =7\end{array}$

Thus, the values of x and y are 7 and 2 respectively.