સમીકરણની સંહતિ $2x + 3y + 4z = 9$,$4x + 9y + 3z = 10,$$5x + 10y + 5z = 11$તો $x$ ની કિમત મેળવો.
$\left| {\,\begin{array}{*{20}{c}}9&3&4\\{10}&9&3\\{11}&{10}&5\end{array}\,} \right| \div \left| {\,\begin{array}{*{20}{c}}2&3&4\\4&9&3\\5&{10}&5\end{array}\,} \right|$
$\left| {\,\begin{array}{*{20}{c}}9&4&3\\{10}&3&9\\{11}&5&{10}\end{array}\,} \right| \div \left| {\,\begin{array}{*{20}{c}}2&3&4\\4&9&3\\5&{10}&5\end{array}\,} \right|$
$\left| {\,\begin{array}{*{20}{c}}9&4&9\\{10}&3&3\\{11}&5&{10}\end{array}\,} \right| \div \left| {\,\begin{array}{*{20}{c}}3&2&4\\9&4&3\\{10}&5&5\end{array}\,} \right|$
એકપણ નહી.
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 $x =$ ........... .
$\Delta = \left| {\,\begin{array}{*{20}{c}}{a + x}&b&c\\b&{x + c}&a\\c&a&{x + b}\end{array}\,} \right|$ નો અવયવ . . . .થાય.
$\left| {\,\begin{array}{*{20}{c}}2&8&4\\{ - 5}&6&{ - 10}\\1&7&2\end{array}\,} \right|$ = . . ..
જો $A=\left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 4\end{array}\right]$ હોય, તો સાબિત કરો કે $|3 A|=27|A|$.
જો $A = \int\limits_1^{\sin \theta } {\frac{t}{{1 + {t^2}}}} dt$ અને $B = \int\limits_1^{\cos ec\theta } {\frac{dt}{{t\left( {1 + {t^2}} \right)}}} $ , (કે જ્યાં $\theta \in \left( {0,\frac{\pi }{2}} \right))$, હોય તો $\left| {\begin{array}{*{20}{c}}
A&{{A^2}}&{ - B}\\
{{e^{A + B}}}&{{B^2}}&{ - 1}\\
1&{{A^2} + {B^2}}&{ - 1}
\end{array}} \right|$ ની કિમંત મેળવો.