The system of linear equations
x + y + z = 2
2x + 3y + 2z = 5
2x + 3y + (a² – 1) z = a + 1 then

Let A = $$\left[ {\matrix{ 1 & 0 & 0 \cr 1 & 1 & 0 \cr 1 & 1 & 1 \cr } } \right]$$ and B = A²⁰. Then the sum of the elements of the first column of B is :

The number of values of k for which the system of linear equations,
(k + 2)x + 10y = k
kx + (k +3)y = k -1
has no solution, is :

If $$\left| {\matrix{ {x - 4} & {2x} & {2x} \cr {2x} & {x - 4} & {2x} \cr {2x} & {2x} & {x - 4} \cr } } \right| = \left( {A + Bx} \right){\left( {x - A} \right)^2}$$

then the ordered pair (A, B) is equal to :