Question

what is the solution of the matrix equation?

[ 5 -2] X= [ 2 ]
[ 2 -1] [-4]

Answer 1

\[\begin{bmatrix}5&-2\\2&-1\end{bmatrix}\begin{bmatrix}x_1\\x_2\end{bmatrix}=\begin{bmatrix}2\\-4\end{bmatrix}\]

\[\left[\begin{array}{cc|c}{}5&-2&2\\2&-1&-4\end{array}\right]\]

Answer 2

perform row operations until you get

\[\left[\begin{array}{cc|c}{}1&0&x_1\\0&1&x_2\end{array}\right]\]

Answer 3

change the first row, first
\[R_1\to R_1-2R_2\]