Use Cramer's Rule to solve the system. $$\left\{ \begin{array} { r }
2 x - y - 3 z = 3 \
x + 3 y - 2 z = - 4 \
7 x + 7 y - 12 z = - 5
\end{array} \right.$$
A) $( 3,1,0 )$
B) $( - 3 , - 1,0 )$
C) $( 2,1,10 )$
D) $( - 3,2,0 )$
E)no solution

Question

Use Cramer's Rule to solve the system. $$\left\{ \begin{array} { r } 
2 x - y - 3 z = 3 \
x + 3 y - 2 z = - 4 \
7 x + 7 y - 12 z = - 5
\end{array} \right.$$
A) $( 3,1,0 )$
B) $( - 3 , - 1,0 )$
C) $( 2,1,10 )$
D) $( - 3,2,0 )$
E)no solution

Quizplus · Accepted Answer

Cramer's Rule is applicable only when the determinant of the coefficient matrix is non-zero. In this case, the determinant of the coefficient matrix is zero, indicating that the system of equations does not have a unique solution. Therefore, Cramer's Rule cannot be used to solve this system, suggesting the possibility of either no solution or infinitely many solutions, but without further analysis, we cannot determine which. Hence, the correct choice is "no solution" based on the information provided.

Use Cramer's Rule to Solve the System {2x−y−3z=3x+3y−2z=−47x+7y−12z=−5\left\{ \begin{array} { r } 2 x - y - 3 z = 3 \\x + 3 y - 2 z = - 4 \\7 x + 7 y - 12 z = - 5\end{array} \right.⎩⎨⎧​2x−y−3z=3x+3y−2z=−47x+7y−12z=−5​

Use Cramer's Rule to Solve the System $\left\{ \begin{array} { r } 2 x - y - 3 z = 3 \\x + 3 y - 2 z = - 4 \\7 x + 7 y - 12 z = - 5\end{array} \right.$