જો $2x + 3y - 5z = 7, \,x + y + z = 6$, $3x - 4y + 2z = 1,$ તો $ x =$
$\left| {\,\begin{array}{*{20}{c}}2&{ - 5}&7\\1&1&6\\3&2&1\end{array}\,} \right| \div \left| {\,\begin{array}{*{20}{c}}7&3&{ - 5}\\6&1&1\\1&{ - 4}&2\end{array}\,} \right|$
$\left| {\,\begin{array}{*{20}{c}}{ - 7}&3&{ - 5}\\{ - 6}&1&1\\{ - 1}&{ - 4}&2\end{array}\,} \right| \div \left| {\,\begin{array}{*{20}{c}}2&3&{ - 5}\\1&1&1\\3&{ - 4}&2\end{array}\,} \right|$
$\left| {\,\begin{array}{*{20}{c}}7&3&{ - 5}\\6&1&1\\1&{ - 4}&2\end{array}\,} \right| \div \left| {\,\begin{array}{*{20}{c}}2&3&{ - 5}\\1&1&1\\3&{ - 4}&2\end{array}\,} \right|$
એકપણ નહી.
ધારો કે સમીકરણ સંહતિ $x+y+k z=2$ ; $2 x+3 y-z=1$ ; $3 x+4 y+2 z=k$ ને અસંખ્ય ઉકેલો છે. $( k +1) x +(2 k -1) y =7$ ; $(2 k +1) x +( k +5) y =10$ ને:
$\,\left| {\,\begin{array}{*{20}{c}}1&1&1\\1&2&3\\1&3&6\end{array}\,} \right| \ne . . . .$
જો $\left| {\,\begin{array}{*{20}{c}}a&b&c\\m&n&p\\x&y&z\end{array}\,} \right| = k$, તો $\left| {\,\begin{array}{*{20}{c}}{6a}&{2b}&{2c}\\{3m}&n&p\\{3x}&y&z\end{array}\,} \right| = $
જો $\left|\begin{array}{cc}x & 2 \\ 18 & x\end{array}\right|=\left|\begin{array}{cc}6 & 2 \\ 18 & 6\end{array}\right|$ હોય, તો $x =$ ........... .
જો રેખાઓ $x + 2ay + a = 0$, $x + 3by + b = 0$ અને $x + 4cy + c = 0$ એ સંગામી હોય તો $a$, $b$ અને $c$ એ . . . . શ્રેણીમાં હોય .