Determine whether the system is inconsistent, dependent, or neither.
-$$\begin{array} { l }
x - y + 2 z = - 2 \
4 x + z = 0 \
- x + y - 2 z = 4
\end{array}$$
A)dependent
B)inconsistent
C)neither

Question

Determine whether the system is inconsistent, dependent, or neither.
-$$\begin{array} { l } 
x - y + 2 z = - 2 \
4 x + z = 0 \
- x + y - 2 z = 4
\end{array}$$
A)dependent
B)inconsistent
C)neither

Quizplus · Accepted Answer

The system is inconsistent because the third equation is a multiple of the first equation with a different constant term, leading to a contradiction.

Determine Whether the System Is Inconsistent, Dependent, or Neither x−y+2z=−24x+z=0−x+y−2z=4\begin{array} { l } x - y + 2 z = - 2 \\4 x + z = 0 \\- x + y - 2 z = 4\end{array}x−y+2z=−24x+z=0−x+y−2z=4​

Determine Whether the System Is Inconsistent, Dependent, or Neither $\begin{array} { l } x - y + 2 z = - 2 \\4 x + z = 0 \\- x + y - 2 z = 4\end{array}$