Inconsistent and Dependent Systems and Their Applications
1 Apply Gaussian Elimination to Systems Without Unique Solutions
-$$\begin{array} { r }
3 x - 2 y + 2 z - w = 2 \
4 x + y + z + 6 w = 8 \
- 3 x + 2 y - 2 z + w = 5 \
5 x + 3 z - 2 w = 1
\end{array}$$
A) $\varnothing$
B) $\left\{ \left( 2,0 , - \frac { 3 } { 37 } , \frac { 9 } { 37 } \right) \right\}$
C) $\left\{ \left( \frac { 1 } { 2 } , 0 , - \frac { 37 } { 3 } , \frac { 37 } { 9 } \right) \right\}$
D) $\left\{ \left( 1 , - \frac { 1 } { 3 } , \frac { 4 } { 9 } , 6 \right) \right\}$

Question

Inconsistent and Dependent Systems and Their Applications
1 Apply Gaussian Elimination to Systems Without Unique Solutions
-$$\begin{array} { r } 
3 x - 2 y + 2 z - w = 2 \
4 x + y + z + 6 w = 8 \
- 3 x + 2 y - 2 z + w = 5 \
5 x + 3 z - 2 w = 1
\end{array}$$
A) $\varnothing$
B) $\left\{ \left( 2,0 , - \frac { 3 } { 37 } , \frac { 9 } { 37 } \right) \right\}$
C) $\left\{ \left( \frac { 1 } { 2 } , 0 , - \frac { 37 } { 3 } , \frac { 37 } { 9 } \right) \right\}$
D) $\left\{ \left( 1 , - \frac { 1 } { 3 } , \frac { 4 } { 9 } , 6 \right) \right\}$

Quizplus · Accepted Answer

The system is inconsistent because the first and third equations are multiples of each other but have different constants on the right-hand side, which means there's no solution that satisfies all equations simultaneously.