Inconsistent and Dependent Systems and Their Applications
1 Apply Gaussian Elimination to Systems Without Unique Solutions
-$$\begin{array} { r }
x - y + z - w = 10 \
- 2 x + 3 y + 5 w = - 28 \
x + 2 y + 8 z + 3 w = - 10 \
x - 4 y - 6 z - 5 w = 30
\end{array}$$
A) $\{ ( - 17 w - 10 , - 13 w - 16,5 w + 4 , w ) \}$
B) $\{ ( 3 w - 2 , - 8 w + 3,4 w + 9 , w ) \}$
C) $\{ ( 24,10 , - 6 , - 2 ) \}$
D) $\varnothing$

Question

Inconsistent and Dependent Systems and Their Applications
1 Apply Gaussian Elimination to Systems Without Unique Solutions
-$$\begin{array} { r } 
x - y + z - w = 10 \
- 2 x + 3 y + 5 w = - 28 \
x + 2 y + 8 z + 3 w = - 10 \
x - 4 y - 6 z - 5 w = 30
\end{array}$$
A) $\{ ( - 17 w - 10 , - 13 w - 16,5 w + 4 , w ) \}$
B) $\{ ( 3 w - 2 , - 8 w + 3,4 w + 9 , w ) \}$
C) $\{ ( 24,10 , - 6 , - 2 ) \}$
D) $\varnothing$

Quizplus · Accepted Answer

The system does not have a unique solution, indicating it is either inconsistent or dependent. The correct answer involves expressions with a parameter (in this case, $w$), which suggests a dependent system with infinitely many solutions parameterized by $w$.