Write the augmented matrix for the system of equations.
-$$\begin{array} { l }
6 x + 9 y + 6 z = 54 \
4 x + 2 y + 7 z = 17 \
3 x - 2 y + 2 z = 2
\end{array}$$
A)
$$\left[ \begin{array} { r r r | r }
6 & 9 & 6 & 54 \
4 & 2 & 7 & 17 \
3 & - 2 & 2 & 2
\end{array} \right]$$
B)
$\left[ \begin{array} { r r r | r } 6 & 4 & 3 & 54 \ 9 & 2 & - 2 & 17 \ 6 & 7 & 2 & 2 \end{array} \right]$
C)
$\left[ \begin{array} { r r r | r } 54 & 6 & 9 & 6 \ 17 & 7 & 2 & 4 \ 2 & 2 & - 2 & 3 \end{array} \right]$
D)
$\left[ \begin{array} { r r r } 6 & 9 & 6 \ 4 & 2 & 7 \ 3 & - 2 & 2 \end{array} \right]$

Question

Write the augmented matrix for the system of equations.
-$$\begin{array} { l } 
6 x + 9 y + 6 z = 54 \
4 x + 2 y + 7 z = 17 \
3 x - 2 y + 2 z = 2
\end{array}$$
A)
$$\left[ \begin{array} { r r r | r } 
6 & 9 & 6 & 54 \
4 & 2 & 7 & 17 \
3 & - 2 & 2 & 2
\end{array} \right]$$
B)
$\left[ \begin{array} { r r r | r } 6 & 4 & 3 & 54 \ 9 & 2 & - 2 & 17 \ 6 & 7 & 2 & 2 \end{array} \right]$
C)
$\left[ \begin{array} { r r r | r } 54 & 6 & 9 & 6 \ 17 & 7 & 2 & 4 \ 2 & 2 & - 2 & 3 \end{array} \right]$
D)
$\left[ \begin{array} { r r r } 6 & 9 & 6 \ 4 & 2 & 7 \ 3 & - 2 & 2 \end{array} \right]$

Quizplus · Accepted Answer

The augmented matrix for a system of equations is created by adding a vertical line and the constants to the coefficient matrix. In this case, option A correctly represents the coefficients and constants in the system. Option B has the correct numbers, but the order of the rows and columns is incorrect. Option C has the correct numbers but the matrix is transposed, and option D is simply the coefficient matrix without the constants.

Write the Augmented Matrix for the System of Equations 6x+9y+6z=544x+2y+7z=173x−2y+2z=2\begin{array} { l } 6 x + 9 y + 6 z = 54 \\4 x + 2 y + 7 z = 17 \\3 x - 2 y + 2 z = 2\end{array}6x+9y+6z=544x+2y+7z=173x−2y+2z=2​

Write the Augmented Matrix for the System of Equations $\begin{array} { l } 6 x + 9 y + 6 z = 54 \\4 x + 2 y + 7 z = 17 \\3 x - 2 y + 2 z = 2\end{array}$