Question

Write each system of linear equations as an augmented matrix.

$\left\{\begin{array}{l}4x+3y=-2\\ x-2y-3z=7\\ 2x-y+2z=-6\end{array}\right.$

Short answer

For the given system of equations$\left\{\begin{array}{l}4x+3y=-2\\ x-2y-3z=7\\ 2x-y+2z=-6\end{array}\right.$, the augmented matrix is given as $\left[\begin{array}{rrrr}4& 3& 0& -2\\ 1& -2& -3& 7\\ 2& -1& 2& -6\end{array}\right]$.

Step-by-step solution

Step 1. Given Information

Consider the system of equations $\left\{\begin{array}{l}4x+3y=-2\\ x-2y-3z=7\\ 2x-y+2z=-6\end{array}\right.$

The objective is to write the system of equations as an augmented matrix.

Step 2. Write augmented matrix

In the augmented matrix, the first equation gives us the first row, the second equation gives us the second row, and the third equation gives us the third row. The vertical line replaces the equal signs. So for the given system, the augmented matrix is

$\left[\begin{array}{rrrr}4& 3& 0& -2\\ 1& -2& -3& 7\\ 2& -1& 2& -6\end{array}\right]$