Question

Write the system of equations corresponding to the

augmented matrix:

$\left[\begin{array}{cccc}3& 2& 4& -6\\ 1& 0& 8& 2\\ -2& 1& 3& -11\end{array}\right]$

Short answer

The system of equation from the augmented matrix will be

$$\begin{gathered} 3x+2y+4z=-6 \\ x+8z=2 \\ -2x+y+3z=-11 \end{gathered}$$

Step-by-step solution

Step 1. Given

$\left[\begin{array}{cccc}3& 2& 4& -6\\ 1& 0& 8& 2\\ -2& 1& 3& -11\end{array}\right]$

Step 2. Calculation

In an augmented matrix all part of varies are written on left side and constant on right side.

$$\begin{gathered} 3x+2y+4z=-6 \\ x+8z=2 \\ -2x+y+3z=-11 \end{gathered}$$