Use Matrices and Gauss-Jordan Elimination to Solve Systems
-$$\begin{aligned}
3 x + 5 y + 2 w & = - 12 \
2 x + 6 z - w & = - 5 \
- 2 y + 3 z - 3 w & = - 3 \
- x + 2 y + 4 z + w & = - 2
\end{aligned}$$
A) $\{ ( - 1 , - 3,0,3 ) \}$
B) $\{ ( 1 , - 3,0,3 ) \}$
C) $\{ ( - 1,3,0 , - 3 ) \}$
D) $\{ ( 1,3,0 , - 3 ) \}$ -

Question

Quizplus · Accepted Answer

To solve the system using Gauss-Jordan elimination, we convert the system of equations into an augmented matrix and then apply row operations to reach reduced row echelon form (RREF). The solution corresponds to the values of $x$, $y$, $z$, and $w$ that satisfy all equations simultaneously. Without performing the detailed steps here, the correct solution set after applying Gauss-Jordan elimination is $\{ ( - 1 , - 3,0,3 ) \}$, indicating that $x = -1$, $y = -3$, $z = 0$, and $w = 3$ are the values that satisfy the given system of equations.