# Write the vector form of the general solution of the given system of linear equations. 3x_1+x_2-x_3+x_4=0 2x_1+2x_2+4x_3-6x_4=0 2x_1+x_2+3x_3-x_4=0

Write the vector form of the general solution of the given system of linear equations.
$3{x}_{1}+{x}_{2}-{x}_{3}+{x}_{4}=0$
$2{x}_{1}+2{x}_{2}+4{x}_{3}-6{x}_{4}=0$
$2{x}_{1}+{x}_{2}+3{x}_{3}-{x}_{4}=0$
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Anonym
$\left[\begin{array}{ccccc}3& 1& -1& 1& 0\\ 2& 2& 4& -6& 0\\ 2& 1& 3& -1& 0\end{array}\right]$
Write the augmented matrix of the coefficients and constants
$\left[\begin{array}{ccccc}1& 0& 0& 2& 0\\ 0& 1& 0& -5& 0\\ 0& 0& 1& 0& 0\end{array}\right]$
Transform the matrix in its reduced row echelon form.
${x}_{1}=-2{x}_{4}$
${x}_{2}=5{x}_{4}$
${x}_{3}=0$

Determine the general solution
$\left[\begin{array}{c}{x}_{1}\\ {x}_{2}\\ {x}_{3}\\ {x}_{4}\end{array}\right]={x}_{4}\left[\begin{array}{c}-2\\ 5\\ 0\\ 1\end{array}\right]$
Rewrite the solution in vector form