 # 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 Chardonnay Felix 2021-09-19 Answered
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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$\left[\begin{array}{ccccc}1& 0& 3& 2& 0\\ 0& 0& 1& -6& 0\end{array}\right]$ Rewrite the corresponding augmented matrix of the system of linear equations.
$\left[\begin{array}{ccccc}1& 3& 0& 2& 0\\ 0& 0& 1& -6& 0\end{array}\right]$Transform the matrix in its reduced row echelon form.
x1=-3x2-2x4
x2=x2 free
x3=6x4
x4=x4 free
Determine the general solution.
$\left[\begin{array}{c}{x}_{1}\\ {x}_{2}\\ {x}_{3}\\ {x}_{4}\end{array}\right]={x}_{2}\left[\begin{array}{c}-3\\ 1\\ 0\\ 0\end{array}\right]+{x}_{4}\left[\begin{array}{c}-2\\ 0\\ 6\\ 1\end{array}\right]$ Express the solutions in vector form."