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If $2x + 3y - 5z = 7, \,x + y + z = 6$, $3x - 4y + 2z = 1,$ then $x =$
$\left| {\,\begin{array}{*{20}{c}}2&{ - 5}&7\\1&1&6\\3&2&1\end{array}\,} \right| \div \left| {\,\begin{array}{*{20}{c}}7&3&{ - 5}\\6&1&1\\1&{ - 4}&2\end{array}\,} \right|$
$\left| {\,\begin{array}{*{20}{c}}{ - 7}&3&{ - 5}\\{ - 6}&1&1\\{ - 1}&{ - 4}&2\end{array}\,} \right| \div \left| {\,\begin{array}{*{20}{c}}2&3&{ - 5}\\1&1&1\\3&{ - 4}&2\end{array}\,} \right|$
$\left| {\,\begin{array}{*{20}{c}}7&3&{ - 5}\\6&1&1\\1&{ - 4}&2\end{array}\,} \right| \div \left| {\,\begin{array}{*{20}{c}}2&3&{ - 5}\\1&1&1\\3&{ - 4}&2\end{array}\,} \right|$
None of these
Solution
(c) For the given set of equation, by Cramer’s Rule
$x = \frac{{{D_x}}}{D} = \left| {\,\begin{array}{*{20}{c}}7&{\,\,3}&{ – 5}\\6&{\,\,1}&{\,\,1}\\1&{ – 4}&{\,\,2}\end{array}\,} \right|\, \div \left| {\,\begin{array}{*{20}{c}}2&{\,\,3}&{ – 5}\\1&{\,\,1}&{\,\,1}\\3&{ – 4}&{\,\,2}\end{array}\,} \right|$.
