$\,\left| {\,\begin{array}{*{20}{c}}1&1&1\\1&2&3\\1&3&6\end{array}\,} \right| \ne . . . .$
$\left| {\,\begin{array}{*{20}{c}}2&1&1\\2&2&3\\2&3&6\end{array}\,} \right|$
$\left| {\,\begin{array}{*{20}{c}}2&1&1\\3&2&3\\4&3&6\end{array}\,} \right|$
$\left| {\begin{array}{*{20}{c}}1&2&1\\1&5&3\\1&9&6\end{array}} \right|$
$\left| {\,\begin{array}{*{20}{c}}3&1&1\\6&2&3\\{10}&3&6\end{array}} \right|\,$
જો $\left|\begin{array}{ll}3 & x \\ x & 1\end{array}\right|=\left|\begin{array}{ll}3 & 2 \\ 4 & 1\end{array}\right|$ હોય, તો $x$ નું મૂલ્ય શોધો.
જો ${A_i} = \left[ {\begin{array}{*{20}{c}}{{a^i}}&{{b^i}}\\{{b^i}}&{{a^i}}\end{array}} \right]$ અને $|a|\, < 1,\,|b|\, < 1$, તો $\sum\limits_{i = 1}^\infty {\det ({A_i})} $= . . .
નિશ્ચાયક $\Delta=\left|\begin{array}{rrr}1 & 2 & 4 \\ -1 & 3 & 0 \\ 4 & 1 & 0\end{array}\right|$ નું મૂલ્ય મેળવો.
સમીકરણની સંહતિ $(k + 1)x + 8y = 4k,$ $kx + (k + 3)y = 3k - 1$ ને અનંત ઉકેલ હોય, તો $k$ ની કિમત મેળવો.
$\left| {\,\begin{array}{*{20}{c}}1&1&1\\1&{{\omega ^2}}&\omega \\1&\omega &{{\omega ^2}}\end{array}\,} \right| = $