Use Cramer s rule to solve the system of equations, if possible. $\left\{ \begin{array} { l }
2 x + y + z = 6 \
x - 2 y + 3 z = 8 \
x + y - 4 z = - 2
\end{array} \right.$
A) $( 1 , - 1,3 )$
B) $( 3 , - 1,1 )$
C) $( 1 , - 3,1 )$
D) dependent
E) inconsistent

Question

Use Cramer s rule to solve the system of equations, if possible. $\left\{ \begin{array} { l } 
2 x + y + z = 6 \
x - 2 y + 3 z = 8 \
x + y - 4 z = - 2
\end{array} \right.$
A) $( 1 , - 1,3 )$
B) $( 3 , - 1,1 )$
C) $( 1 , - 3,1 )$
D) dependent
E) inconsistent

Quizplus · Accepted Answer

Cramer's rule involves calculating determinants. The determinant of the coefficient matrix is non-zero, allowing us to solve the system. Calculating the determinants for x, y, and z gives the solution (3, -1, 1).

Use Cramer S Rule to Solve the System of Equations {2x+y+z=6x−2y+3z=8x+y−4z=−2\left\{ \begin{array} { l } 2 x + y + z = 6 \\x - 2 y + 3 z = 8 \\x + y - 4 z = - 2\end{array} \right.⎩⎨⎧​2x+y+z=6x−2y+3z=8x+y−4z=−2​

Use Cramer S Rule to Solve the System of Equations $\left\{ \begin{array} { l } 2 x + y + z = 6 \\x - 2 y + 3 z = 8 \\x + y - 4 z = - 2\end{array} \right.$