$l,m,n$ are the ${p^{th}},{q^{th}}$and ${r^{th}}$term of a G.P., all positive, then $\left| {\,\begin{array}{*{20}{c}}{\log l}&{p\,\,\,\,\,\begin{array}{*{20}{c}}1\end{array}}\\{\log m}&{q\,\,\,\,\,\begin{array}{*{20}{c}}1\end{array}}\\{\log n}&{r\,\,\,\,\,\begin{array}{*{20}{c}}1\end{array}}\end{array}\,} \right|$ equals
$-1$
$2$
$1$
$0$
If the system of linear equations $x + 2ay + az = 0$ $x + 3by + bz = 0$ $x + 4cy + cz = 0$ has a non-zero solution, then $a, b, c$
One of the roots of the given equation $\left| {\,\begin{array}{*{20}{c}}{x + a}&b&c\\b&{x + c}&a\\c&a&{x + b}\end{array}\,} \right| = 0$ is
The value of the determinant $\left| {\,\begin{array}{*{20}{c}}1&a&{b + c}\\1&b&{c + a}\\1&c&{a + b}\end{array}\,} \right|$is
If $A=\left[\begin{array}{ll}1 & 2 \\ 4 & 2\end{array}\right],$ then show that $|2 A|=4|A|$.
The existance of the unique solution of the system of equations$2x + y + z = \beta $ , $10x - y + \alpha z = 10$ and $4x+ 3y-z =6$ depends on