\([1,2,-1,1,0]\) Write the augmented matrix of the coefficients and constants

\([1,2,-1,1,0] \)Transform the matrix in its reduced row echelon form.

x1=-2x2+x3-x4

x2=x2 free

x3=x3 free

x4=x4 free

Determine the general solution

\(\begin{bmatrix}x_1 \\x_2 \\x_3 \\x_4 \end{bmatrix}=x_2\begin{bmatrix}-2 \\1 \\0 \\0 \end{bmatrix}+x_3\begin{bmatrix}1 \\0 \\0 \\0 \end{bmatrix}-x_4\begin{bmatrix}-1 \\0 \\0 \\1 \end{bmatrix}\)Rewrite the solution in vector form