Use the Gauss-Jordan method to solve the system of equations.
-$-3 x-y-9 z=-75$
$3 x+5 y-2 z=44$
$-8 \mathrm{x}-6 \mathrm{y}+\mathrm{z}=-95$
A) No solution
B) $(8,6,5)$
C) $(-8,6,16)$
D) $(8,5,6)$

Question

Quizplus · Accepted Answer

The system of equations can be written in matrix form as:$$\begin{bmatrix}-3 & -1 & -9 \\ 3 & 5 & -2 \\ -8 & -6 & 1\end{bmatrix}\begin{bmatrix}x \\ y \\ z\end{bmatrix}=\begin{bmatrix}-75 \\ 44 \\ -95\end{bmatrix}$$Using the Gauss-Jordan method, we can reduce the matrix to:$$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}\begin{bmatrix}x \\ y \\ z\end{bmatrix}=\begin{bmatrix}8 \\ 6 \\ 5\end{bmatrix}$$Therefore, the solution to the system of equations is $x=8, y=6, z=5$.

Use the Gauss-Jordan Method to Solve the System of Equations −3x−y−9z=−75-3 x-y-9 z=-75−3x−y−9z=−75

Use the Gauss-Jordan Method to Solve the System of Equations $-3 x-y-9 z=-75$