Use Gauss-Jordan elimination to solve the linear system and determine whether the system has a unique solution, no solution, or infinitely many solutions. If the system has infinitely many solutions, describe the solution as an ordered
triple involving variable z.
-$$\begin{aligned}
4 x - y + 3 z & = 12 \
x + 4 y + 6 z & = - 32 \
5 x + 3 y + 9 z & = 20
\end{aligned}$$
A)(8, -7, -2)
B)(-8, -7, 9)
C)no solution
D)(2, -7, -1)

Question

Quizplus · Accepted Answer

The system has no solution because when applying Gauss-Jordan elimination, we find that the matrix form of the system leads to a row indicating a contradiction (e.g., a row of the form [0 0 0 | c] with c ≠ 0), which means the system of equations is inconsistent.

Use Gauss-Jordan Elimination to Solve the Linear System and Determine 4x−y+3z=12x+4y+6z=−325x+3y+9z=20\begin{aligned}4 x - y + 3 z & = 12 \\x + 4 y + 6 z & = - 32 \\5 x + 3 y + 9 z & = 20\end{aligned}4x−y+3zx+4y+6z5x+3y+9z​=12=−32=20​

Use Gauss-Jordan Elimination to Solve the Linear System and Determine $\begin{aligned}4 x - y + 3 z & = 12 \\x + 4 y + 6 z & = - 32 \\5 x + 3 y + 9 z & = 20\end{aligned}$