To construct the augmented matrix for the given system of equations, we must first rewrite the system of equations with the same order for terms on the left hand side.
The given equations are:
1) 2x + (5y - z)/2 = 4, which rearranges to 2x + 5y - z = 8.
2) 3(7z - 6x) + y - 8 = 9, which simplifies to -18x + y + 21z = 17.
3) x - (5 + z) = 4y, which rearranges to x - 4y - z = 5.
The coefficients of equations in the form of ax + by + cz = d forms the entries of our augmented matrix, and if no term exists, the coefficient is considered as 0.
So, we form the augmented matrix:
[ [ 2, 5, -1, 4 ],
[-6, 1, 21, 17 ],
[ 1, -4, -1, 0 ]
]
Each row represents one of the original equations and each column corresponds to a specific variable (x, y, z) and the constant on the right side of the equations.