Determine whether the system corresponding to the given augmented matrix is dependent or inconsistent. If it is
dependent, give the solution.
-$$\left[ \begin{array} { l l l | l }
1 & 0 & - 5 & 3 \
0 & 1 & 9 & - 7 \
0 & 0 & 0 & 0
\end{array} \right]$$
A) dependent; $( 3 , - 7 , - 5 )$
B) dependent; $( 3 + 5 z , y = - 7 - 9 z , z )$
C) dependent; $( 3 - 5 z , - 7 + 9 z , z )$
D) inconsistent

Question

Determine whether the system corresponding to the given augmented matrix is dependent or inconsistent. If it is
dependent, give the solution.
-$$\left[ \begin{array} { l l l | l } 
1 & 0 & - 5 & 3 \
0 & 1 & 9 & - 7 \
0 & 0 & 0 & 0
\end{array} \right]$$
A) dependent; $( 3 , - 7 , - 5 )$
B) dependent; $( 3 + 5 z , y = - 7 - 9 z , z )$
C) dependent; $( 3 - 5 z , - 7 + 9 z , z )$
D) inconsistent

Quizplus · Accepted Answer

The system is dependent because the last row of the augmented matrix is all zeros. The solution is given by the first two rows of the matrix, which correspond to the equations $x = 3$ and $y = -7$. The third variable, $z$, is free, so it can take on any value.

Determine Whether the System Corresponding to the Given Augmented Matrix [10−53019−70000]\left[ \begin{array} { l l l | l } 1 & 0 & - 5 & 3 \\0 & 1 & 9 & - 7 \\0 & 0 & 0 & 0\end{array} \right]​100​010​−590​3−70​​

Determine Whether the System Corresponding to the Given Augmented Matrix $\left[ \begin{array} { l l l | l } 1 & 0 & - 5 & 3 \\0 & 1 & 9 & - 7 \\0 & 0 & 0 & 0\end{array} \right]$