Apply Gaussian Elimination to Systems Without Unique Solutions
Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists.
-$$\begin{array} { r r }
x + y + z + w = & 7 \
3 x - 2 z + 5 w = & 11 \
- 4 x + 3 y + w = & 4 \
- x - y - z - w = & 6
\end{array}$$
A) $\varnothing$
B) $\left\{ \left( \frac { 3 } { 2 } , 1 , \frac { 1 } { 3 } , - 2 \right) \right\}$
C) $\left\{ \left( \frac { 7 } { 4 } , - \frac { 1 } { 2 } , 5 , - \frac { 1 } { 6 } \right) \right\}$
D) $\left\{ \left( - 11 , \frac { 7 } { 19 } , \frac { 6 } { 19 } , - 4 \right) \right\}$

Question

Apply Gaussian Elimination to Systems Without Unique Solutions
Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists.
-$$\begin{array} { r r } 
x + y + z + w = & 7 \
3 x - 2 z + 5 w = & 11 \
- 4 x + 3 y + w = & 4 \
- x - y - z - w = & 6
\end{array}$$
A) $\varnothing$
B) $\left\{ \left( \frac { 3 } { 2 } , 1 , \frac { 1 } { 3 } , - 2 \right) \right\}$
C) $\left\{ \left( \frac { 7 } { 4 } , - \frac { 1 } { 2 } , 5 , - \frac { 1 } { 6 } \right) \right\}$
D) $\left\{ \left( - 11 , \frac { 7 } { 19 } , \frac { 6 } { 19 } , - 4 \right) \right\}$

Quizplus · Accepted Answer

The system of equations is inconsistent because the first and last equations are contradictory: adding the first equation to the last gives $0 = 13$, which is impossible.