If the system of equations, $a^2 x - ay = 1 - a$ & $bx + (3 - 2b) y = 3 + a$ possess a unique solution $x = 1, y = 1$ then :
$a = 1 ; b = - 1$
$a = - 1 , b = 1$
$a = 0 , b = 0$
none
If $a,b,c$ and $d $ are complex numbers, then the determinant $\Delta = \left| {\,\begin{array}{*{20}{c}}2&{a + b + c + d}&{ab + cd}\\{a + b + c + d}&{2(a + b)(c + d)}&{ab(c + d) + cd(a + b)}\\{ab + cd}&{ab(c + d) + cd(a + d)}&{2abcd}\end{array}} \right|$is
The number of values of $\alpha$ for which the system of equations: $x+y+z=\alpha$ ; $\alpha x+2 \alpha y+3 z=-1$ ; $x+3 \alpha y+5 z=4$ is inconsistent, is
Find equation of line joining $(1,2)$ and $(3,6)$ using determinates
The greatest value of $c \in R$ for which the system of linear equations
$x - cy - cz = 0 \,\,;\,\, cx - y + cz = 0 \,\,;\,\, cx + cy - z = 0 $ has a non -trivial solution, is
$\left| {\,\begin{array}{*{20}{c}}{11}&{12}&{13}\\{12}&{13}&{14}\\{13}&{14}&{15}\end{array}\,} \right| = $