Answer::
[tex]\mleft[\begin{array}{rrr|r}1 & 1 & -1 & 8 \\ 6 & -4 & 0 & 4 \\ 6 & 2 & -1 & 2\end{array}\mright][/tex]
Explanation:
For any system of equations, an augmented matrix is a matrix of numbers where:
• Each row represents the constants((both the coefficients and the constant) from one equation; and
,
• Each column represents all the coefficients for a single variable.
Given the system of equations:
[tex]\mleft\{\begin{array}{r}x+y-z=8 \\ 6x-4y=4 \\ 6x+2y-z=2\end{array}\mright.[/tex]
Writing this as a product of matrices gives:
[tex]\mleft(\begin{array}{rrr}1 & 1 & -1 \\ 6 & -4 & 0 \\ 6 & 2 & -1\end{array}\mright)\mleft(\begin{array}{rrr}x \\ y \\ z\end{array}\mright)=\mleft(\begin{array}{rrr}8 \\ 4 \\ 2\end{array}\mright)[/tex]
Therefore, the augmented matrix is:
[tex]\mleft[\begin{array}{rrr|r}1 & 1 & -1 & 8 \\ 6 & -4 & 0 & 4 \\ 6 & 2 & -1 & 2\end{array}\mright][/tex]
