Write the system of equations corresponding to each augmented matrix. Then perform the indicated row operation(s) on the given augmented matrix.

The given matrix and operation is

The given matrix has three rows. So, it represents a system of three linear equations. The 3 columns to the left of vertical bar indicate that the system has three variables.

Let the variables be x, y and z. Then system of linear equation corresponding to the given matrix is as follows,

$$\begin{gathered} x-3y+3z=-5 \\ -4x-5y-3z=-5 \\ -3x-2y+4z=6 \end{gathered}$$

Apply the first-row operation on the given augmented matrix and simplify,

role="math" localid="1647341781870" $$\begin{gathered} \left[\begin{array}{cccc}1& -3& 3|& -5\\ -4& -5& -3|& -5\\ -3& -2& 4|& 6\end{array}\right]\to \left[\begin{array}{cccc}1& -3& 3|& -5\\ 4\left(1\right)+(-4)& 4(-3)+(-5)& 4\left(3\right)+(-3)|& 4(-5)+(-5)\\ -3& -2& 4|& 6\end{array}\right] \\ \to \left[\begin{array}{cccc}1& -3& 3|& -5\\ 0& -17& 9|& -25\\ -3& -2& 4|& 6\end{array}\right] \end{gathered}$$

Now, apply the second-row operation on the given matrix and simplify,

$$\begin{gathered} \left[\begin{array}{cccc}1& -3& 3|& -5\\ -4& -5& -3|& -5\\ -3& -2& 4|& 6\end{array}\right]\to \left[\begin{array}{cccc}1& -3& 3|& -5\\ -4& -5& -3|& -5\\ 3\left(1\right)+(-3)& 3(-3)+(-2)& 3\left(3\right)+4|& 3(-5)+6\end{array}\right] \\ \to \left[\begin{array}{cccc}1& -3& 3|& -5\\ -4& -5& -3|& -5\\ 0& -11& 13|& -9\end{array}\right] \end{gathered}$$