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

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

$\left[1,2,-1,1,0\right]$ Write the augmented matrix of the coefficients and constants
$\left[1,2,-1,1,0\right]$Transform the matrix in its reduced row echelon form.
x1=-2x2+x3-x4
x2=x2 free
x3=x3 free
x4=x4 free
Determine the general solution
$\left[\begin{array}{c}{x}_{1}\\ {x}_{2}\\ {x}_{3}\\ {x}_{4}\end{array}\right]={x}_{2}\left[\begin{array}{c}-2\\ 1\\ 0\\ 0\end{array}\right]+{x}_{3}\left[\begin{array}{c}1\\ 0\\ 0\\ 0\end{array}\right]-{x}_{4}\left[\begin{array}{c}-1\\ 0\\ 0\\ 1\end{array}\right]$Rewrite the solution in vector form