Perform the row operation$($s$)$ on the given augmented matrix.

$($a$)R_3=-5r_1+r_3$

$($b$)R_4=3r_1+r_4$

$\left[\begin{array}{ccccc}1& 1& -1& 1& 3\\ 0& -4& 3& -2& 0\\ 3& 0& -2& -5& 2\\ -4& 2& 0& 1& -5\end{array}\right]$

$\left[\begin{array}{ccccc}1& 1& -1& 1& 3\\ 0& -4& 3& -2& 0\\ -2& -5& 3& -10& -13\\ -1& 5& -3& 4& 4\end{array}\right]$

$\left[\begin{array}{ccccc}1& 1& -1& 1& 3\\ 0& -4& 3& -2& 0\\ 8& 5& -7& 0& 17\\ -1& 5& -3& 4& 4\end{array}\right]$

$\left[\begin{array}{ccccc}1& 1& -1& 1& 3\\ 0& -4& 3& -2& 0\\ -2& -5& 3& -10& -3\\ -1& 5& -3& 4& 4\end{array}\right]$

$\left[\begin{array}{ccccc}1& 1& -1& 1& 3\\ 0& -4& 3& -2& 0\\ -2& -5& 3& -10& -13\\ -4& 2& 0& 1& -5\end{array}\right]$