Use the Gauss-Jordan method to solve the system of equations.
-$
\begin{array}{l}
8 x+9 y-z=48 \
x-4 y+7 z=65 \
2 x+y+z=22
\end{array}
$
A) $ (6,1,9) $
B) $ (6,9,1) $
C) $ (-6,1,12) $
D) No solution

Question

Quizplus · Accepted Answer

To solve the system of equations using the Gauss-Jordan method, we first write the augmented matrix of the system and then apply row operations to transform it into reduced row echelon form (RREF). The system of equations is:$$ \begin{align*}8x + 9y - z &= 48 \x - 4y + 7z &= 65 \2x + y + z &= 22\end{align*} $$The augmented matrix is:$$ \left[ \begin{array}{ccc|c}8 & 9 & -1 & 48 \1 & -4 & 7 & 65 \2 & 1 & 1 & 22\end{array} \right] $$Applying row operations to simplify this matrix into RREF gives us:$$ \left[ \begin{array}{ccc|c}1 & 0 & 0 & 6 \0 & 1 & 0 & 1 \0 & 0 & 1 & 9\end{array} \right] $$This corresponds to the solution $x = 6$, $y = 1$, and $z = 9$, which matches choice (A) $ (6,1,9) $.

Use the Gauss-Jordan Method to Solve the System of Equations 8x+9y−z=48x−4y+7z=652x+y+z=22\begin{array}{l}8 x+9 y-z=48 \\x-4 y+7 z=65 \\2 x+y+z=22\end{array}8x+9y−z=48x−4y+7z=652x+y+z=22​

Use the Gauss-Jordan Method to Solve the System of Equations $\begin{array}{l}8 x+9 y-z=48 \\x-4 y+7 z=65 \\2 x+y+z=22\end{array}$