જો $\left| {\,\begin{array}{*{20}{c}}{y + z}&{x - z}&{x - y}\\{y - z}&{z - x}&{y - x}\\{z - y}&{z - x}&{x + y}\end{array}\,} \right| = k\,xyz$, તો $k$ મેળવો.

સાબિત કરો કે, $\Delta=\left|\begin{array}{ccc}
(y+z)^{2} & x y & z x \\
x y & (x+z)^{2} & y z \\
x z & y z & (x+y)^{2}
\end{array}\right|=2 x y z(x+y+z)^{3}$

જો $\left| {\,\begin{array}{*{20}{c}}{{{(b + c)}^2}}&{{a^2}}&{{a^2}}\\{{b^2}}&{{{(c + a)}^2}}&{{b^2}}\\{{c^2}}&{{c^2}}&{{{(a + b)}^2}}\end{array}\,} \right| = k\,abc{(a + b + c)^3}$, તો $k$ મેળવો.

જો $A$, $B$ અને  $C$ ત્રિકોણના ખૂણા હોય તો નિશ્ચાયક 

$\left| {\begin{array}{*{20}{c}}
  { - 1 + \cos B}&{\cos C + \cos B}&{\cos B} \\ 
  {\cos C + \cos A}&{ - 1 + \cos A}&{\cos A} \\ 
  { - 1 + \cos B}&{ - 1 + \cos A}&{ - 1} 
\end{array}} \right|$ ની કિમંત મેળવો.

$\left| {\,\begin{array}{*{20}{c}}{1 + x}&1&1\\1&{1 + y}&1\\1&1&{1 + z}\end{array}\,} \right| = $

$\left| {\,\begin{array}{*{20}{c}}{a - b - c}&{2a}&{2a}\\{2b}&{b - c - a}&{2b}\\{2c}&{2c}&{c - a - b}\end{array}\,} \right| = $