Determine the form of the augmented matrix that represents the following system of equations. \[ \begin{aligned} 4 w+5 x+y+3 z & =3 \\ -4 w-3 x-3 y-4 z & =3 \\ -2 x+y-5 z & =-1 \\ -5 w-2 x-3 y+4 z & =-4 \end{aligned} \] $\left(\begin{array}{rrrr|r}4 & 5 & 1 & 3 & 3 \\ -4 & -3 & -3 & -4 & 3 \\ 0 & -2 & 1 & -5 & -1 \\ -5 & -2 & -3 & 4 & -4\end{array}\right)$ $\left(\begin{array}{rrrr|r}5 & 5 & 4 & 4 & 3 \\ 3 & 3 & 3 & 2 & 3 \\ 2 & 0 & -1 & -1 & -1 \\ -3 & -4 & -4 & -5 & -4\end{array}\right)$ $\left(\begin{array}{rrrr|r}-4 & -5 & -1 & -3 & 3 \\ 4 & 3 & 3 & 4 & 3 \\ 0 & 2 & -1 & 5 & -1 \\ 5 & 2 & 3 & -4 & -4\end{array}\right)$ $\left(\begin{array}{rrrr|r}-5 & -5 & -4 & -4 & 3 \\ -3 & -3 & -3 & -2 & 3 \\ -2 & 0 & 1 & 1 & -1 \\ 3 & 4 & 4 & 5 & -4\end{array}\right)$

Step 1 ：Determine the form of the augmented matrix that represents the following system of equations.

Step 2 ：\[\begin{aligned}4 w+5 x+y+3 z & =3 \-4 w-3 x-3 y-4 z & =3 \-2 x+y-5 z & =-1 \-5 w-2 x-3 y+4 z & =-4\end{aligned}\]

Step 3 ：An augmented matrix is a matrix obtained by appending the columns of two given matrices, usually for the purpose of performing the same elementary row operations on each of the given matrices. In this case, the augmented matrix will be a representation of the system of equations, where each row represents an equation and each column represents a coefficient of a variable.

Step 4 ：The augmented matrix that represents the given system of equations is:

Step 5 ：\[\boxed{\begin{aligned}\left(\begin{array}{rrrr|r}4 & 5 & 1 & 3 & 3 \-4 & -3 & -3 & -4 & 3 \0 & -2 & 1 & -5 & -1 \-5 & -2 & -3 & 4 & -4\end{array}\right)\end{aligned}}\]