Solve the system using determinants.
-$$\begin{array} { l }
3 x + y - 3 z = 6 \
- x + 3 y + 2 z = 6 \
- 5 x - 5 x + 4 z = - 18
\end{array}$$
A)(-3, 3, -3)
B)(0, 0, -2)
C)infinite number of solutions
D)no solution

Question

Solve the system using determinants.
-$$\begin{array} { l } 
3 x + y - 3 z = 6 \
- x + 3 y + 2 z = 6 \
- 5 x - 5 x + 4 z = - 18
\end{array}$$
A)(-3, 3, -3)
B)(0, 0, -2)
C)infinite number of solutions
D)no solution

Quizplus · Accepted Answer

To solve the system using determinants, we first check the determinant of the coefficient matrix. If the determinant is zero, the system may have either no solution or an infinite number of solutions, depending on the determinants of the matrices formed by replacing one column of the coefficient matrix with the column of constants. However, the given system has an error in its formulation: the third equation appears to be incorrectly stated as "- 5 x - 5 x + 4 z = - 18", which likely contains a typo since it combines terms of x incorrectly. Assuming this is a mistake and without a clear way to correct it, we cannot accurately compute determinants. However, the presence of a mistake in the system's formulation suggests that the system as presented cannot be solved as intended, leading to the conclusion that it might be intended to demonstrate a situation where the system does not behave normally (e.g., has an infinite number of solutions due to dependency between equations). Given the error and assuming the intention was to present a special case, the most fitting answer based on the provided options and typical outcomes when dealing with determinants and systems of equations would be an infinite number of solutions, acknowledging that the actual algebraic solution process cannot be correctly applied to the given system due to the error in its presentation.

Solve the System Using Determinants 3x+y−3z=6−x+3y+2z=6−5x−5x+4z=−18\begin{array} { l } 3 x + y - 3 z = 6 \\- x + 3 y + 2 z = 6 \\- 5 x - 5 x + 4 z = - 18\end{array}3x+y−3z=6−x+3y+2z=6−5x−5x+4z=−18​

Solve the System Using Determinants $\begin{array} { l } 3 x + y - 3 z = 6 \\- x + 3 y + 2 z = 6 \\- 5 x - 5 x + 4 z = - 18\end{array}$