Convert the system

$$\begin{array}{rcrcrcr}-2 x_1 & - & 6 x_{2} & + & x_{3} & = & -3 \\ x_1 & + & 3 x_{2} & & & = & 1 \\-4 x_1 & - & 12 x_{2} & + & x_{3} & = & -5\end{array}$$

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:

Echelon form:

Is the system consistent? select yes no

Solution: $(x_1,x_2,x_3) = \bigg($ $+$ $s_1$, $+$ $s_1$, $+$ $s_1\bigg)$

Help: To enter a matrix use [[ ],[ ]] . For example, to enter the $2\times 3$ matrix

$$\left[\begin{array}{ccc} 1 & 2 & 3 \\ 6 & 5 & 4 \end{array}\right]$$

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 $(5 + 0s_1, -2 + 0s_1, 1+ 0s_1)$. If the system is inconsistent, you do not have to type anything in the "Solution" answer blanks.