question_answer

If \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}z=0,{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}z=0\] \[{{a}_{3}}x+{{b}_{3}}y+{{c}_{3}}z=0\] and \[\left| \,\begin{matrix}    {{a}_{1}} & {{b}_{1}} & {{c}_{1}}  \\    {{a}_{2}} & {{b}_{2}} & {{c}_{2}}  \\    {{a}_{3}} & {{b}_{3}} & {{c}_{3}}  \\ \end{matrix}\, \right|=0,\]then the given system has  [Roorkee 1990]

A) One trivial and one non-trivial solution

B) No solution

C) One solution

D) Infinite solution