To write the augmented matrix for the given system of equations, we first need to rearrange each equation in the standard form $ax + by + cz = d$, where the variables $x$, $y$, and $z$ are on the left side of the equation, and the constant term is on the right.

Given System of Equations:

1. $-3 - z = -4x$
2. $-3 = x - 5y$
3. $-3 + 2y + 5x = -z$

Step 1: Rewrite each equation in standard form

First Equation:

$-3 - z = -4x \Rightarrow 4x + 0y - z = -3$

Second Equation:

$-3 = x - 5y \Rightarrow -x + 5y + 0z = -3$

Third Equation:

$-3 + 2y + 5x = -z \Rightarrow 5x + 2y + z = 3$

Now, the system is:

1. $4x + 0y - z = -3$
2. $-x + 5y + 0z = -3$
3. $5x + 2y + z = 3$

Step 2: Write the augmented matrix

The augmented matrix will take the form: