# Write the vector form of the general solution of the given system of linear equations.x_1+4x_4=0 , x_2-2x_4

Write the vector form of the general solution of the given system of linear equations.
$$x_1+4x_4=0$$
$$x_2−2x_4$$

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$$\begin{bmatrix}1&0&4&0 \\0&1&-2&0 \end{bmatrix}$$ 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.