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

Write the vector form of the general solution of the given system of linear equations.
${x}_{1}+2{x}_{2}-{x}_{3}=0$
${x}_{1}+{x}_{2}+{x}_{3}=0$
${x}_{1}+3{x}_{2}-3{x}_{3}=0$
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Szeteib
$\left[\begin{array}{cccc}1& 2& -1& 0\\ 1& 1& 1& 0\\ 1& 3& -3& 0\end{array}\right]$
Write the augmented matrix of the coefficients and constants
$\left[\begin{array}{cccc}1& 0& 3& 0\\ 0& 1& -2& 0\\ 0& 0& 0& 0\end{array}\right]$
Transform the matrix in its reduced row echelon form.
${x}_{1}=-3{x}_{3}$
${x}_{2}=2{x}_{3}$

Determine the general solution
$\left[\begin{array}{c}{x}_{1}\\ {x}_{2}\\ {x}_{3}\end{array}\right]={x}_{4}\left[\begin{array}{c}-3\\ 2\\ 1\end{array}\right]$
Rewrite the solution in vector form