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

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

\(x_1=-2x_2+x_3-x_4\)

\(x_2=x_2\) free

\(x_3=x_3\) free

\(x_4=x_4\) free

Determine the general solution

Rewrite the solution in vector form

\(\begin{bmatrix}x_1 \\x_2\\x_3\\x_4 \end{bmatrix}=x_2\begin{bmatrix}-2 \\1\\0\\0\end{bmatrix}+x_3\begin{bmatrix}1 \\0\\0\\0\end{bmatrix}-x_4\begin{bmatrix}-1 \\0\\0\\1\end{bmatrix}\)