Form the augmented matrix for the system of linear equations below. $\left\{ \begin{array} { r }
6 x + y + z = 2 \
4 x + 4 y + 4 z = 9 \
8 x + y + 4 z = - 7
\end{array} \right.$
A) $\left[ \begin{array} { c }
2 \
9 \
- 7
\end{array} \right]$
B) $\left[ \begin{array} { l l l }
6 & 4 & 8 \
1 & 4 & 1 \
1 & 4 & 4
\end{array} \right]$
C) $\left[ \begin{array} { c c c c }
6 & 1 & 1 & 2 \
4 & 4 & 4 & 9 \
8 & 1 & 4 & - 7
\end{array} \right]$
D) $\left[ \begin{array} { l l l }
6 & 1 & 1 \
4 & 4 & 4 \
8 & 1 & 4
\end{array} \right]$
E) $\left[ \begin{array} { c c c }
6 & 4 & 8 \
1 & 4 & 1 \
1 & 4 & 4 \
2 & 9 & - 7
\end{array} \right]$

Question

Form the augmented matrix for the system of linear equations below. $\left\{ \begin{array} { r } 
6 x + y + z = 2 \
4 x + 4 y + 4 z = 9 \
8 x + y + 4 z = - 7
\end{array} \right.$
A) $\left[ \begin{array} { c } 
2 \
9 \
- 7
\end{array} \right]$
B) $\left[ \begin{array} { l l l } 
6 & 4 & 8 \
1 & 4 & 1 \
1 & 4 & 4
\end{array} \right]$
C) $\left[ \begin{array} { c c c c } 
6 & 1 & 1 & 2 \
4 & 4 & 4 & 9 \
8 & 1 & 4 & - 7
\end{array} \right]$
D) $\left[ \begin{array} { l l l } 
6 & 1 & 1 \
4 & 4 & 4 \
8 & 1 & 4
\end{array} \right]$
E) $\left[ \begin{array} { c c c } 
6 & 4 & 8 \
1 & 4 & 1 \
1 & 4 & 4 \
2 & 9 & - 7
\end{array} \right]$

Quizplus · Accepted Answer

The augmented matrix for a system of linear equations is formed by arranging the coefficients of the variables and the constant terms in a rectangular array, with each equation forming a row. Therefore, the correct augmented matrix for the given system is:
$$\left[ \begin{array} { c c c c } 
6 & 1 & 1 & 2 \
4 & 4 & 4 & 9 \
8 & 1 & 4 & - 7
\end{array} ight]$$
Choice C is the only option that matches this augmented matrix.

Form the Augmented Matrix for the System of Linear Equations {6x+y+z=24x+4y+4z=98x+y+4z=−7\left\{ \begin{array} { r } 6 x + y + z = 2 \\4 x + 4 y + 4 z = 9 \\8 x + y + 4 z = - 7\end{array} \right.⎩⎨⎧​6x+y+z=24x+4y+4z=98x+y+4z=−7​

Form the Augmented Matrix for the System of Linear Equations $\left\{ \begin{array} { r } 6 x + y + z = 2 \\4 x + 4 y + 4 z = 9 \\8 x + y + 4 z = - 7\end{array} \right.$