The problem is asking to construct the augmented matrix corresponding to the given system of equations. Here's how we solve it step-by-step.

Step 1: Write the given equations clearly

The system of equations is:

1. $\frac{2x + 6y - z}{3} = 8$
2. $2(7z - 6x) + y - 9 = 3$
3. $x - (5 + z) = 3y$

Step 2: Rewrite the equations in standard form $Ax + By + Cz = D$

We rearrange each equation to isolate the terms involving $x, y, z$ on one side and the constant on the other.

Equation 1:

$\frac{2x + 6y - z}{3} = 8$ Multiply through by 3: $2x + 6y - z = 24$

Equation 2:

$2(7z - 6x) + y - 9 = 3$ Expand $2(7z - 6x)$: $14z - 12x + y - 9 = 3$ Simplify: $-12x + y + 14z = 12$

Equation 3:

$x - (5 + z) = 3y$ Distribute the negative sign: $x - 5 - z = 3y$ Rearrange: $x - 3y - z = 5$

Step 3: Form the augmented matrix

The augmented matrix includes the coefficients of $x, y, z$ (in order) from each equation, and the constants on the right-hand side.

From the three equations:

1. $2x + 6y - z = 24$
2. $-12x + y + 14z = 12$
3. $x - 3y - z = 5$

The augmented matrix is: