Question

Write the system of equations corresponding to the given augmented matrix.

$\left[\begin{array}{rrrr}1& 2& 5& -2\\ 5& 0& -3& 8\\ 2& -1& 0& 0\end{array}\right]$

Short answer

The system of equations is$\left\{\begin{array}{rl}x+2y+5z& =-2\\ 5x-3z& =8\\ 2x-y& =0\end{array}\right.$

Step-by-step solution

Step 1. Given information

The given augmented matrix is$\left[\begin{array}{rrrr}1& 2& 5& -2\\ 5& 0& -3& 8\\ 2& -1& 0& 0\end{array}\right]$

Step 2. Convert augmented matrix into the system of equations.

If the two variables are $x$and $y$, then the system of equations is

$\left\{\begin{array}{rl}x+2y+5z& =-2\\ 5x-3z& =8\\ 2x-y& =0\end{array}\right.$