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.
-$$\begin{array} { r }
x + 3 y + 2 z = 11 \
4 y + 9 z = - 12 \
x + 7 y + 11 z = - 1
\end{array}$$
A) $\left\{ \left( \frac { 19 z } { 4 } + 20 , - \frac { 9 z } { 4 } - 3 , z \right) \right\}$
B) $\left\{ \left( \frac { 19 z } { 4 } + 20 , - \frac { 9 z } { 4 } + 3 , z \right) \right\}$
C) $\left\{ \left( \frac { 19 z } { 4 } + 20 , \frac { 9 z } { 4 } + 3 , z \right) \right\}$
D) $\left\{ \left( - \frac { 19 \mathrm { z } } { 4 } + 20 , - \frac { 9 \mathrm { z } } { 4 } + 3 , \mathrm { z } \right) \right\}$

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.
-$$\begin{array} { r } 
x + 3 y + 2 z = 11 \
4 y + 9 z = - 12 \
x + 7 y + 11 z = - 1
\end{array}$$
A) $\left\{ \left( \frac { 19 z } { 4 } + 20 , - \frac { 9 z } { 4 } - 3 , z \right) \right\}$
B) $\left\{ \left( \frac { 19 z } { 4 } + 20 , - \frac { 9 z } { 4 } + 3 , z \right) \right\}$
C) $\left\{ \left( \frac { 19 z } { 4 } + 20 , \frac { 9 z } { 4 } + 3 , z \right) \right\}$
D) $\left\{ \left( - \frac { 19 \mathrm { z } } { 4 } + 20 , - \frac { 9 \mathrm { z } } { 4 } + 3 , \mathrm { z } \right) \right\}$

Quizplus · Accepted Answer

Gaussian elimination reveals the system has infinitely many solutions, parameterized by $z$. The correct solution set is obtained by expressing $x$ and $y$ in terms of $z$.

Apply Gaussian Elimination to Systems Without Unique Solutions Use Gaussian x+3y+2z=114y+9z=−12x+7y+11z=−1\begin{array} { r } x + 3 y + 2 z = 11 \\4 y + 9 z = - 12 \\x + 7 y + 11 z = - 1\end{array}x+3y+2z=114y+9z=−12x+7y+11z=−1​

Apply Gaussian Elimination to Systems Without Unique Solutions
Use Gaussian $\begin{array} { r } x + 3 y + 2 z = 11 \\4 y + 9 z = - 12 \\x + 7 y + 11 z = - 1\end{array}$