Given:
[tex]\begin{gathered} 2x+\frac{5y-z}{4}=9...............(1) \\ 2(6z-4x)+y-8=6...............(2) \\ x-(5+z)=5y...............(3) \end{gathered}[/tex]
To find:
The augmented matrix
Explanation:
Let us write equations in the standard form.
From 1,
[tex]8x+5y-z=36...........(4)[/tex]
From 2,
[tex]\begin{gathered} 12z-8x+y-8=6 \\ 12z-8x+y=14 \\ -8x+y+12z=14...........(5) \end{gathered}[/tex]
From 3,
[tex]\begin{gathered} \begin{equation*} x-(5+z)=5y \end{equation*} \\ x-5-z=5y \\ x-5y-z=5............(6) \end{gathered}[/tex]
Using the equation (4), (5), and (6),
The augmented matrix,
[tex]\begin{bmatrix}{8} & {5} & {-1} & {36} \\ {-8} & {1} & {12} & {14} \\ {1} & {-5} & {-1} & {5} \\ {} & {} & {} & {}\end{bmatrix}[/tex]
Final answer:
The augmented matrix,
[tex]\begin{bmatrix}{8} & {5} & {-1} & {36} \\ {-8} & {1} & {12} & {14} \\ {1} & {-5} & {-1} & {5} \\ {} & {} & {} & {}\end{bmatrix}[/tex]
