Given that the matrix

$$\left[\begin{array}{rrrr} 2 & 6 & 4 & 0 \\ 2 & 0 & 5 & 1 \\ 2 & -7 & -2 & 5\end{array}\right]$$

is the augmented matrix for a linear system, use technology to perform the row operations needed to transform the matrix to reduced echelon form. Then determine if the system is consistent and if it is, find all solutions to the system.

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