Apply Gaussian Elimination to Systems with More Variables than Equations
-$$\begin{array} { l }
x + y + z = 9 \
2 x - 3 y + 4 z = 7
\end{array}$$
A) $\left\{ \left( - \frac { 7 } { 5 } \mathrm { z } + \frac { 34 } { 5 } , \frac { 2 } { 5 } \mathrm { z } + \frac { 11 } { 5 } , \mathrm { z } \right) \right\}$
B) $\left\{ \left( \frac { 3 } { 5 } z + \frac { 16 } { 5 } , - \frac { 8 } { 5 } z + \frac { 29 } { 5 } , z \right) \right\}$
C) $\left\{ \left( \frac { 27 } { 5 } , \frac { 13 } { 5 } , 1 \right) \right\}$
D) $\varnothing$

Question

Apply Gaussian Elimination to Systems with More Variables than Equations
-$$\begin{array} { l } 
x + y + z = 9 \
2 x - 3 y + 4 z = 7
\end{array}$$
A) $\left\{ \left( - \frac { 7 } { 5 } \mathrm { z } + \frac { 34 } { 5 } , \frac { 2 } { 5 } \mathrm { z } + \frac { 11 } { 5 } , \mathrm { z } \right) \right\}$
B) $\left\{ \left( \frac { 3 } { 5 } z + \frac { 16 } { 5 } , - \frac { 8 } { 5 } z + \frac { 29 } { 5 } , z \right) \right\}$
C) $\left\{ \left( \frac { 27 } { 5 } , \frac { 13 } { 5 } , 1 \right) \right\}$
D) $\varnothing$

Quizplus · Accepted Answer

The system has more variables than equations, indicating infinite solutions. By applying Gaussian elimination, we can express two variables (x and y) in terms of the third variable (z), leading to a parametric solution set as given in option A.

Apply Gaussian Elimination to Systems with More Variables Than Equations x+y+z=92x−3y+4z=7\begin{array} { l } x + y + z = 9 \\2 x - 3 y + 4 z = 7\end{array}x+y+z=92x−3y+4z=7​

Apply Gaussian Elimination to Systems with More Variables Than Equations $\begin{array} { l } x + y + z = 9 \\2 x - 3 y + 4 z = 7\end{array}$