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 coefficients of the variables in each equation and their respective constants on the right side of the equation. The first row of the matrix (0, 2, 6, 3) translates to $2y + 6z = 3$, the second row (1, 0, 0, -9) translates to $x = -9$, and the third row (2, 3, 0, 0) translates to $2x + 3y = 0$. This matches option D.

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 $\left[ \begin{array} { c c c c } 0 & 2 & 6 & 3 \\1 & 0 & 0 & - 9 \\2 & 3 & 0 & 0\end{array} \right]$