Chapter 2.3, Problem 20E

To determine

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

Answer to Problem 20E

  $\begin{array}{l}x=2\\ y=-1\end{array}$

Explanation of Solution

Given information:

The given matrix equation is as follows:

  $\left[\begin{array}{c}4x-3y\\ x+y\end{array}\right]=\left[\begin{array}{c}11\\ 1\end{array}\right]$

Calculation:

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

Matrices can be represented as follows:

  $\begin{array}{c}4x-3y=11\mathrm{...}\left(1\right)\\ x+y=1\mathrm{...}\left(2\right)\end{array}$

Now, solve equation (2) as follows:

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

Put the value of $x=1-y$ in equation (1) and solve as follows:

  $\begin{array}{c}4\left(1-y\right)-3y=11\\ 4-4y-3y=11\\ 4-7y=11\\ 7y=4-11\\ 7y=-7\\ y=-1\end{array}$

Put the value of y in equation 3 and solve as follows:

  $\begin{array}{c}x=1-y\\ =1-\left(-1\right)\\ =1+1\\ =2\end{array}$

Thus, the values of x and y are 2 and $-1$ respectively.