(1 point) Convert the system
$x_1 - 3x_2 - 4x_3 = -2$
$-2x_1 + 8x_2 + 10x_3 = 8$
to an augmented matrix. Then reduce the system to echelon form and determine if the system is consistent. If the system in consistent, then find all
solutions.
Augmented matrix: $\begin{bmatrix} 1 & -3 & -4 & -2 \ -2 & 8 & 10 & 8 \end{bmatrix}$
Echelon form: $\begin{bmatrix} 1 & 0 & -1 & 4 \ 0 & 1 & 1 & 2 \end{bmatrix}$
Is the system consistent? yes
Solution: $(x_1, x_2, x_3) = ($4$ + $1$ $s_1$, $2$ + $-2$ $s_1$, $0$ + $1$ $s_1)$
Help: To enter a matrix use [[][]]. For example, to enter the 2 x 3 matrix
$\begin{bmatrix} 1 & 2 & 3 \ 6 & 5 & 4 \end{bmatrix}$
you would type [[1,2,3],[6,5,4]], so each inside set of [] represents a row. If there is no free variable in the solution, then type 0 in each of the answer
blanks directly before each $s_1$. For example, if the answer is $(x_1, x_2, x_3) = (5, -2, 1)$, then you would enter (5 + 0$s_1$, -2 + 0$s_1$, 1 + 0$s_1$). If the system
is inconsistent, you do not have to type anything in the \"Solution\" answer blanks.
