Question

The system of linear equations : $x+y+z=0,2x+y-z=0,3x+2y=0$ has :

• A. no solution
• B. a unique solution
• C. an infinitely many solution
• D. None of these

Answer 1

Answer: (C)

The system is homogenuous system.
$\therefore$ it has either unique solution or infinitemany solution depend on $|A|$
$\therefore \left|A\right|=\left|\begin{array}{ccc}1& 1& 1\\ 2& 1& -1\\ 3& 2& 0\end{array}\right|$
$=2-3+1=0$