If the system of linear equations $2x + 2y + 3z = a$ ; $3x - y + 5z = b$ ; $x - 3y + 2z = c$ Where $a, b, c$ are non zero real numbers, has more than one solution, then
$b \,-\, c \,+\, a = 0$
$b\, -\, c\, -\,a = 0$
$a \,+\, b\, +\, c = 0$
$b \,+ \,c\, -\,a = 0$
$\left| {\,\begin{array}{*{20}{c}}1&5&\pi \\{{{\log }_e}e}&5&{\sqrt 5 }\\{{{\log }_{10}}10}&5&e\end{array}\,} \right| = $
The value of $\left| {\,\begin{array}{*{20}{c}}{{1^2}}&{{2^2}}&{{3^2}}\\{{2^2}}&{{3^2}}&{{4^2}}\\{{3^2}}&{{4^2}}&{{5^2}}\end{array}\,} \right|$ is
If $\left| {\,\begin{array}{*{20}{c}}a&b&0\\0&a&b\\b&0&a\end{array}\,} \right| = 0$, then
If $D_1$ and $D_2$ are two $3 \times 3$ diagonal matrices, then
If ${D_p} = \left| {\,\begin{array}{*{20}{c}}p&{15}&8\\{{p^2}}&{35}&9\\{{p^3}}&{25}&{10}\end{array}\,} \right|$, then ${D_1} + {D_2} + {D_3} + {D_4} + {D_5} = $