Question

Write the system of equations that corresponds to the augmented matrix:$\left[\begin{array}{rrrr}1& -1& 2& 3\\ 2& 1& -2& 1\\ 4& -1& 2& 0\end{array}\right]$

Short answer

System of equations that corresponds to given augmented matrix is$\left\{\begin{array}{l}x-y+2z=3\\ 2x+y-2z=1\\ 4x-y+2z=0\end{array}\right.$

Step-by-step solution

Step 1. Given Information.

Given Augmented matrix is$\left[\begin{array}{rrrr}1& -1& 2& 3\\ 2& 1& -2& 1\\ 4& -1& 2& 0\end{array}\right]$

Step 2. Writing Augmented matrix into System of equations.

We remember that each row corresponds to an equation and that each entry is a coefficient of a variable or the constant.

The vertical line replaces the equal sign.

We know it will translate into a system of three equations with three variables.

$\left[\begin{array}{rrrr}1& -1& 2& 3\\ 2& 1& -2& 1\\ 4& -1& 2& 0\end{array}\right]\left\{\begin{array}{l}x-y+2z=3\\ 2x+y-2z=1\\ 4x-y+2z=0\end{array}\right.$