Solve the homogeneous system. $$\left( \begin{array} { r }
3 x + y + z = 0 \
x - y + 2 z = 0 \
4 x - 5 y - 2 z = 0
\end{array} \right)$$
A) (0, 0, 0)
B) inconsistent
C) dependent

Question

Solve the homogeneous system. $$\left( \begin{array} { r } 
3 x + y + z = 0 \
x - y + 2 z = 0 \
4 x - 5 y - 2 z = 0
\end{array} \right)$$
A) (0, 0, 0)
B) inconsistent
C) dependent

Quizplus · Accepted Answer

The system is homogeneous, so it has the trivial solution (0, 0, 0). The determinant of the coefficient matrix is 0, so the system is dependent.

Solve the Homogeneous System (3x+y+z=0x−y+2z=04x−5y−2z=0)\left( \begin{array} { r } 3 x + y + z = 0 \\x - y + 2 z = 0 \\4 x - 5 y - 2 z = 0\end{array} \right)​3x+y+z=0x−y+2z=04x−5y−2z=0​​

Solve the Homogeneous System $\left( \begin{array} { r } 3 x + y + z = 0 \\x - y + 2 z = 0 \\4 x - 5 y - 2 z = 0\end{array} \right)$