Suppose the system of equations \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}z={{d}_{1}}\] \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}z={{d}_{2}}\] \[{{a}_{3}}x+{{b}_{3}}y+{{c}_{3}}z={{d}_{3}}\] has a unique solution \[({{x}_{0}},{{y}_{0}},{{z}_{0}})\]. If \[{{x}_{0}}=0,\] then which one of the following is correct?

• A. \[\left| \begin{matrix}    {{a}_{1}} & {{b}_{1}} & {{c}_{1}}  \\    {{a}_{2}} & {{b}_{2}} & {{c}_{2}}  \\    {{a}_{3}} & {{b}_{3}} & {{c}_{3}}  \\ \end{matrix} \right|=0\]
• B. \[\left| \begin{matrix}    {{d}_{1}} & {{b}_{1}} & {{c}_{1}}  \\    {{d}_{2}} & {{b}_{2}} & {{c}_{2}}  \\    {{d}_{3}} & {{b}_{3}} & {{c}_{3}}  \\ \end{matrix} \right|=0\]
• C. \[\left| \begin{matrix}    {{d}_{1}} & {{a}_{1}} & {{c}_{1}}  \\    {{d}_{2}} & {{a}_{2}} & {{c}_{2}}  \\    {{d}_{3}} & {{a}_{3}} & {{c}_{3}}  \\ \end{matrix} \right|=0\]
• D. \[\left| \begin{matrix}    {{d}_{1}} & {{a}_{1}} & {{b}_{1}}  \\    {{d}_{2}} & {{a}_{2}} & {{b}_{2}}  \\    {{d}_{3}} & {{a}_{3}} & {{b}_{3}}  \\ \end{matrix} \right|=0\]