Inconsistent and Dependent Systems and Their Applications
1 Apply Gaussian Elimination to Systems Without Unique Solutions
-$$\begin{array} { r r }
x + y + z & = 9 \
2 x - 3 y + 4 z & = 7 \
x - 4 y + 3 z & = - 2
\end{array}$$
A) $\left\{ \left( - \frac { 7 z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } + \frac { 11 } { 5 } , z \right) \right\}$
B) $\left\{ \left( \frac { z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } + \frac { 11 } { 5 } , z \right) \right\}$
C) $\left\{ \left( - \frac { 7 z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } - \frac { 11 } { 5 } , z \right) \right\}$
D) $\left\{ \left( \frac { 7 z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } - \frac { 11 } { 5 } , \mathrm { z } \right) \right\}$

Question

Inconsistent and Dependent Systems and Their Applications
1 Apply Gaussian Elimination to Systems Without Unique Solutions
-$$\begin{array} { r r } 
x + y + z & = 9 \
2 x - 3 y + 4 z & = 7 \
x - 4 y + 3 z & = - 2
\end{array}$$
A) $\left\{ \left( - \frac { 7 z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } + \frac { 11 } { 5 } , z \right) \right\}$
B) $\left\{ \left( \frac { z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } + \frac { 11 } { 5 } , z \right) \right\}$
C) $\left\{ \left( - \frac { 7 z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } - \frac { 11 } { 5 } , z \right) \right\}$
D) $\left\{ \left( \frac { 7 z } { 5 } + \frac { 34 } { 5 } , \frac { 2 z } { 5 } - \frac { 11 } { 5 } , \mathrm { z } \right) \right\}$

Quizplus · Accepted Answer

After applying Gaussian elimination, the system reduces to a parameterized form with $z$ as the parameter, showing that there are infinitely many solutions depending on the value of $z$. The correct parameterization of $x$ and $y$ in terms of $z$ is given in option A.

Inconsistent and Dependent Systems and Their Applications 1 Apply Gaussian x+y+z=92x−3y+4z=7x−4y+3z=−2\begin{array} { r r } x + y + z & = 9 \\2 x - 3 y + 4 z & = 7 \\x - 4 y + 3 z & = - 2\end{array}x+y+z2x−3y+4zx−4y+3z​=9=7=−2​

Inconsistent and Dependent Systems and Their Applications
1 Apply Gaussian $\begin{array} { r r } x + y + z & = 9 \\2 x - 3 y + 4 z & = 7 \\x - 4 y + 3 z & = - 2\end{array}$