A) a unique solution; \[x=0,y=0,z=0\]
B) infinite solutions
C) no solution
D) finite number of non-zero solutions
Correct Answer: B
Solution :
The given system of equations an \[x+y+z=0,\] \[2x+3y+z=0,\] and \[x+2y=0\] Here, \[\left| \begin{matrix} 1 & 1 & 1 \\ 2 & 3 & 1 \\ 1 & 2 & 0 \\ \end{matrix} \right|=1\,(0-2)-1\,(0-1)\,+1\,(4-3)\] \[=-2+1+1=0\] \[\therefore \]This system has infinite solutions.
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