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## Homework Statement

Find a 3x3 matrix A that satisfies the following equation where x, y, and z can be any numbers.

## A \begin{vmatrix}

x \\

y \\

z

\end{vmatrix}

= \begin{vmatrix}

x + y \\

x - y \\

0

\end{vmatrix}##

## Homework Equations

## The Attempt at a Solution

I attempted to solve this like we learned in class, with gaussian elimination, but it obviously doesn't work in this scenario, because all of the coefficients in the matrix are literal in this sense.

I found the correct matrix intuitively, but I want to know how to do it properly for future, more complex problems, I've looked at the book, but couldn't find any sample problems regarding this type of solution.

## A = \begin{vmatrix}

a & b & c\\

d & e & f \\

g & h & i

\end{vmatrix}## <-- literal coefficients, not sure how to continue.