# 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

$$[1,2,-1,1,0]$$ Write the augmented matrix of the coefficients and constants
$$[1,2,-1,1,0]$$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
$$\begin{bmatrix}x_1 \\x_2 \\x_3 \\x_4 \end{bmatrix}=x_2\begin{bmatrix}-2 \\1 \\0 \\0 \end{bmatrix}+x_3\begin{bmatrix}1 \\0 \\0 \\0 \end{bmatrix}-x_4\begin{bmatrix}-1 \\0 \\0 \\1 \end{bmatrix}$$Rewrite the solution in vector form