Solve the system of equations by using an inverse matrix.
-$$\begin{aligned}
9 x - y + 9 z & = 92 \
- 7 x + 3 z & = - 27 \
7 y + z & = 54
\end{aligned}$$
A) $\varnothing$
B) $( 6,5,7 )$
C) $( - 6,7,12 )$
D) $( 6,7,5 )$

Question

Quizplus · Accepted Answer

To solve the system using an inverse matrix, we first write it in matrix form $AX = B$, where $A$ is the coefficient matrix, $X$ is the variable matrix, and $B$ is the constant matrix. We find the inverse of $A$ and multiply it by $B$ to find $X$. The solution is $(6,7,5)$.

Solve the System of Equations by Using an Inverse Matrix 9x−y+9z=92−7x+3z=−277y+z=54\begin{aligned}9 x - y + 9 z & = 92 \\- 7 x + 3 z & = - 27 \\7 y + z & = 54\end{aligned}9x−y+9z−7x+3z7y+z​=92=−27=54​

Solve the System of Equations by Using an Inverse Matrix $\begin{aligned}9 x - y + 9 z & = 92 \\- 7 x + 3 z & = - 27 \\7 y + z & = 54\end{aligned}$