# Write the vector form of the general solution of the given system of linear equations.x_1+3x_2+2x_4=0, x_3-6x_4=0

Write the vector form of the general solution of the given system of linear equations.
x1+3x2+2x4=0
x3−6x4=0

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$$\begin{bmatrix}1 & 0 & 3 & 2 & 0 \\0 & 0 & 1 & -6 & 0 \end{bmatrix}$$ Rewrite the corresponding augmented matrix of the system of linear equations.
$$\begin{bmatrix}1 & 3 & 0 & 2 & 0 \\0 & 0 & 1 & -6 & 0 \end{bmatrix}$$Transform the matrix in its reduced row echelon form.
x1=-3x2-2x4
x2=x2 free
x3=6x4
x4=x4 free
Determine the general solution.
$$\begin{bmatrix}x_1 \\x_2 \\x_3 \\x_4 \end{bmatrix}=x_2\begin{bmatrix}-3 \\1 \\0 \\0 \end{bmatrix}+x_4\begin{bmatrix}-2 \\0 \\6 \\1 \end{bmatrix}$$ Express the solutions in vector form."