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

A)  one trivial and one non-trivial solution

B)  no solution

C)  one solution

D)  infinite solution