I need to find the values for the given variables to make the below equation consistent. I've tried setting the corresponding entries equal to each other and solving the system for a, b, c, d, but I'm not sure how to do that if there are many other x variables. How do I go about answering this question?
\begin{bmatrix}x_{1}-3x_{2}+2x_{4}&-2x_{4}+5x_{5}+b\\3x_{1}-x_{3}+7x_{5}&9x_{2}+6x_{4}-d\end{bmatrix} = \begin{bmatrix}-2x_{5}+a&-2x_{1}+6x_{2}+x_{3}\\9x_{2}+c&3x_{1}-2x_{3}+8x_{5}\end{bmatrix}
Here what to do for $a$
You have $x_{1}-3x_{2}+2x_{4}=-2x_{5}+a$
so $a=x_{1}-3x_{2}+2x_{4}+2x_{5}$.
You can try $b,c,d$