Use Cramer's rule to solve the system.
-$$\begin{aligned}
6 x - 7 y - z & = - 53 \
x - 8 y + 9 z & = 19 \
- 3 x + y + z & = 11
\end{aligned}$$
A) $\{ ( 2,8,9 ) \}$
B) $\{ ( 8,9,8 ) \}$
C) $\{ ( 2 , - 8 , - 9 ) \}$
D) $\{ ( 3,6,9 ) \}$

Question

Quizplus · Accepted Answer

Cramer's rule involves calculating determinants of matrices. For this system, the determinant of the coefficient matrix and the determinants of matrices with columns replaced by the constants on the right side of the equations are calculated. The solution $\{ ( 2,8,9 ) \}$ is found by applying Cramer's rule correctly to the given system of equations.

Use Cramer's Rule to Solve the System 6x−7y−z=−53x−8y+9z=19−3x+y+z=11\begin{aligned}6 x - 7 y - z & = - 53 \\x - 8 y + 9 z & = 19 \\- 3 x + y + z & = 11\end{aligned}6x−7y−zx−8y+9z−3x+y+z​=−53=19=11​

Use Cramer's Rule to Solve the System $\begin{aligned}6 x - 7 y - z & = - 53 \\x - 8 y + 9 z & = 19 \\- 3 x + y + z & = 11\end{aligned}$