Write the augmented matrix for the system of equations.
-$$\begin{array} { r }
x - 5 y + z = 11 \
y + 7 z = 19 \
z = 15
\end{array}$$
A)
$\left[ \begin{array} { r r r | r } 1 & - 5 & 1 & 11 \ 0 & 1 & 7 & 19 \ 0 & 0 & 1 & 15 \end{array} \right]$
B)
$\left[ \begin{array} { r r r | r } 0 & - 5 & 0 & 11 \ 0 & 0 & 7 & 19 \ 0 & 0 & 0 & 15 \end{array} \right]$
C)
$\left[ \begin{array} { l l l | l } 1 & 5 & 1 & 11 \ 0 & 1 & 7 & 19 \ 0 & 0 & 1 & 15 \end{array} \right]$
D)
$\left[ \begin{array} { r r r | r } 1 & - 5 & 1 & 11 \ 1 & 1 & 7 & 19 \ 1 & 1 & 1 & 15 \end{array} \right]$

Question

Write the augmented matrix for the system of equations.
-$$\begin{array} { r } 
x - 5 y + z = 11 \
y + 7 z = 19 \
z = 15
\end{array}$$
A)
$\left[ \begin{array} { r r r | r } 1 & - 5 & 1 & 11 \ 0 & 1 & 7 & 19 \ 0 & 0 & 1 & 15 \end{array} \right]$
B)
$\left[ \begin{array} { r r r | r } 0 & - 5 & 0 & 11 \ 0 & 0 & 7 & 19 \ 0 & 0 & 0 & 15 \end{array} \right]$
C)
$\left[ \begin{array} { l l l | l } 1 & 5 & 1 & 11 \ 0 & 1 & 7 & 19 \ 0 & 0 & 1 & 15 \end{array} \right]$
D)
$\left[ \begin{array} { r r r | r } 1 & - 5 & 1 & 11 \ 1 & 1 & 7 & 19 \ 1 & 1 & 1 & 15 \end{array} \right]$

Quizplus · Accepted Answer

The augmented matrix should have the coefficients of the variables on the left and the constants on the right. The first row of the matrix corresponds to the first equation, which has coefficients 1, -5, and 1 for x, y, and z respectively, and a constant of 11. The second row corresponds to the second equation, with coefficients 0, 1, and 7 for x, y, and z respectively, and a constant of 19. The third row corresponds to the third equation, which has coefficients 0, 0, and 1 for x, y, and z respectively, and a constant of 15. The best choice is A because it correctly represents the system of equations.

Write the Augmented Matrix for the System of Equations x−5y+z=11y+7z=19z=15\begin{array} { r } x - 5 y + z = 11 \\y + 7 z = 19 \\z = 15\end{array}x−5y+z=11y+7z=19z=15​

Write the Augmented Matrix for the System of Equations $\begin{array} { r } x - 5 y + z = 11 \\y + 7 z = 19 \\z = 15\end{array}$