\(\begin{bmatrix}1&0&4&0 \\0&1&-2&0 \end{bmatrix}\) Rewrite the corresponding augmented matrix of the system of linear equations.

\(\begin{bmatrix}1&0&4&0 \\0&1&-2&0 \end{bmatrix}\)Transform the matrix in its reduced row echelon form.

\(x_1=-4x_4\)

\(x_2=2x_4\)

\(x_4=x_4\) free

Determine the general solution.

\([x_1,x_2,x_4]=x_4[-4,2,1]\) Express the solutions in vector form.