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\[
x_j  = \frac{{\det \left( {\begin{array}{*{20}c}
   {a_{11} } & {} & {} & {} & {} & {} & {}  \\
   {} & {} & {} & {} & {} & {} & {}  \\
   {} & {} & {} & {} & {} & {} & {}  \\
\end{array}} \right)}}{{}}
\]