Question 15
Find the general solution of the linear system whose augmented matrix is the following.
$\begin{bmatrix} 1 & 0 & 2 & 0 & 0 & 8 \\ 0 & 0 & 0 & 0 & -5 & 0 \\ 0 & 1 & -2 & -4 & 0 & -8 \\ 1 & 1 & 0 & -4 & -5 & 0 \end{bmatrix}$
a. Find the RREF:
b. Select the basic variable(s) from the list below.
$x_1$ $x_2$ $x_3$ $x_4$ $x_5$
c. Select the free variable(s) from the list below.
$x_1$ $x_2$ $x_3$ $x_4$ $x_5$
d. State the general solution of the system, writing basic variables in terms of the free variables. If a variable is a free variable, write "free" (without the quotes).
$x_1 =$
$x_2 =$
$x_3 =$
$x_4 =$
$x_5 =$
```