Use an inverse matrix to find the solution to the system.
-$$\left\{ \begin{array} { c }
- 4 x + 3 y - z = - 3 \
x - 6 y + 8 z = - 5 \
8 x + y + z = 51
\end{array} \right.$$
A) $x = 5 , y = 7 , z = 4$
B) $x = - 5 , y = 7 , z = 10$
C) $x = 5 , y = 4 , z = 7$
D) $x = - 5 , y = 10 , z = 7$

Question

Use an inverse matrix to find the solution to the system.
-$$\left\{ \begin{array} { c } 
- 4 x + 3 y - z = - 3 \
x - 6 y + 8 z = - 5 \
8 x + y + z = 51
\end{array} \right.$$
A) $x = 5 , y = 7 , z = 4$
B) $x = - 5 , y = 7 , z = 10$
C) $x = 5 , y = 4 , z = 7$
D) $x = - 5 , y = 10 , z = 7$

Quizplus · Accepted Answer

The system of equations can be represented in matrix form as AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix. By finding the inverse of A and multiplying it by B, we can solve for X. The correct solution, after performing these calculations, is $x = 5 , y = 7 , z = 4$.

Use an Inverse Matrix to Find the Solution to the System