Write the system of equations for which the given matrix is the augmented matrix. $$\left[ \begin{array} { c c c c }
0 & 2 & 6 & 3 \
1 & 0 & 0 & - 9 \
2 & 3 & 0 & 0
\end{array} \right]$$
A) $\left\{ \begin{aligned}
y + 6 z & = 3 \
z & = - 9 \
2 x - 3 y & = 0
\end{aligned} \right.$

B) $\left\{ \begin{aligned}
2 x + 6 z & = 3 \
x & = - 9 \
x + 3 y & = 0
\end{aligned} \right.$

C) $\left\{ \begin{aligned}
2 x + 6 z & = 3 \
z & = - 9 \
2 y + 3 z & = 0
\end{aligned} \right.$

D) $\left\{ \begin{aligned}
2 y + 6 z & = 3 \
x & = - 9 \
2 x + 3 y & = 0
\end{aligned} \right.$

E)none

Question

Write the system of equations for which the given matrix is the augmented matrix. $$\left[ \begin{array} { c c c c } 
0 & 2 & 6 & 3 \
1 & 0 & 0 & - 9 \
2 & 3 & 0 & 0
\end{array} \right]$$
A) $\left\{ \begin{aligned}
y + 6 z & = 3 \
z & = - 9 \
2 x - 3 y & = 0
\end{aligned} \right.$

B) $\left\{ \begin{aligned}
2 x + 6 z & = 3 \
x & = - 9 \
x + 3 y & = 0
\end{aligned} \right.$

C) $\left\{ \begin{aligned}
2 x + 6 z & = 3 \
z & = - 9 \
2 y + 3 z & = 0
\end{aligned} \right.$

D) $\left\{ \begin{aligned}
2 y + 6 z & = 3 \
x & = - 9 \
2 x + 3 y & = 0
\end{aligned} \right.$

E)none

Quizplus · Accepted Answer

The augmented matrix corresponds to the system of equations where each row represents an equation and the columns (except the last one) represent the coefficients of the variables in order. The last column represents the constants on the right side of the equations. The correct system is D, as it directly matches the structure of the given matrix.

Write the System of Equations for Which the Given Matrix [0263100−92300]\left[ \begin{array} { c c c c } 0 & 2 & 6 & 3 \\1 & 0 & 0 & - 9 \\2 & 3 & 0 & 0\end{array} \right]​012​203​600​3−90​​

Write the System of Equations for Which the Given Matrix $\left[ \begin{array} { c c c c } 0 & 2 & 6 & 3 \\1 & 0 & 0 & - 9 \\2 & 3 & 0 & 0\end{array} \right]$