यदि $\left| {\,\begin{array}{*{20}{c}}a&b&c\\m&n&p\\x&y&z\end{array}\,} \right| = k$, तो $\left| {\,\begin{array}{*{20}{c}}{6a}&{2b}&{2c}\\{3m}&n&p\\{3x}&y&z\end{array}\,} \right| = $

यदि $A =\left[\begin{array}{ll}1 & 2 \\ 4 & 2\end{array}\right],$ तो दिखाइए $|2 A |=4 \mid A$

माना $D = \left| {\,\begin{array}{*{20}{c}}{{a_1}}&{{b_1}}&{{c_1}}\\{{a_2}}&{{b_2}}&{{c_2}}\\{{a_3}}&{{b_3}}&{{c_3}}\end{array}\,} \right|$ and $D' = \left| {\,\begin{array}{*{20}{c}}{{a_1} + p{b_1}}&{{b_1} + q{c_1}}&{{c_1} + r{a_1}}\\{{a_2} + p{b_2}}&{{b_2} + q{c_2}}&{{c_2} + r{a_2}}\\{{a_3} + p{b_3}}&{{b_3} + q{c_3}}&{{c_3} + r{a_3}}\end{array}\,} \right|$, तो

यदि समीकरण निकाय $3x - 2y + z = 0$, $\lambda x - 14y + 15z = 0$, $x + 2y + 3z = 0$ अशून्य हल रखता है, तब $\lambda  = $

$\left| {\,\begin{array}{*{20}{c}}{19}&{17}&{15}\\9&8&7\\1&1&1\end{array}\,} \right| = $

यदि $\Delta_{ r }=\left|\begin{array}{ccc} r & 2 r -1 & 3 r -2 \\ \frac{ n }{2} & n -1 & a \\ \frac{1}{2} n ( n -1) & ( n -1)^{2} & \frac{1}{2}( n -1)(3 n +4)\end{array}\right|$ हैं, तो $\sum_{ r =1}^{ n -1} \Delta_{ r }$ का मान