Apply Gaussian Elimination to Systems with More Variables than Equations
-$$\begin{aligned}
2 x + y + 2 z - 4 w & = 10 \
x + 3 y + 2 z - 11 w & = 17 \
3 x + y + 7 z - 21 w & = 0
\end{aligned}$$
A) $\{ ( - 3 w + 5,2 w + 6,4 w - 3 , w ) \}$
B) $\{ ( 3 w + 5,6 w + 6 , - 4 w - 3 , w ) \}$
C) $\{ ( w + 5,8 w + 4 , - 3 w - 2 , w ) \}$
D) $\{ ( w - 5,8 w - 4 , - 3 w + 2 , w ) \}$

Question

Quizplus · Accepted Answer

Gaussian elimination on this system reveals that it has infinitely many solutions, parameterized by $w$. The correct parameterization matches choice A, where each variable $x, y, z$ is expressed in terms of $w$.

Apply Gaussian Elimination to Systems with More Variables Than Equations 2x+y+2z−4w=10x+3y+2z−11w=173x+y+7z−21w=0\begin{aligned}2 x + y + 2 z - 4 w & = 10 \\x + 3 y + 2 z - 11 w & = 17 \\3 x + y + 7 z - 21 w & = 0\end{aligned}2x+y+2z−4wx+3y+2z−11w3x+y+7z−21w​=10=17=0​

Apply Gaussian Elimination to Systems with More Variables Than Equations $\begin{aligned}2 x + y + 2 z - 4 w & = 10 \\x + 3 y + 2 z - 11 w & = 17 \\3 x + y + 7 z - 21 w & = 0\end{aligned}$