# The reduced row echelon form of the augmented matrix of a system of linear eqs. is given. Determine whether this system of linear eqs. is consistent

The reduced row echelon form of the augmented matrix of a system of linear equations is given. Determine whether this system of linear equations is consistent and, if so, find its general solution. Write the solution in vector form. $\left[\begin{array}{ccccc}1& 0& 0& -3& 0\\ 0& 1& 0& -4& 0\\ 0& 0& 1& 5& 0\end{array}\right]$

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x1-3x4=0
x2-4x4=0
x3+5x4=0
x1=3x4
x2=4x4
x3=-5x4
x4, free
x1=3t
x2=4t
x3=-5t
x4=t
$x=\left[\begin{array}{c}0\\ 0\\ 0\\ 0\end{array}\right]+t\left[\begin{array}{c}3\\ 4\\ -5\\ 1\end{array}\right]=t\left[\begin{array}{c}3\\ 4\\ -5\\ 1\end{array}\right]$

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