An ordered pair ($$\alpha $$, $$\beta $$) for which the system of linear equations
(1 + $$\alpha $$) x + $$\beta $$y + z = 2
$$\alpha $$x + (1 + $$\beta $$)y + z = 3
$$\alpha $$x + $$\beta $$y + 2z = 2
has a unique solution, is :

If  $$\left| {\matrix{ {a - b - c} & {2a} & {2a} \cr {2b} & {b - c - a} & {2b} \cr {2c} & {2c} & {c - a - b} \cr } } \right|$$

      = (a + b + c) (x + a + b + c)², x $$ \ne $$ 0,

then x is equal to :

Let A and B be two invertible matrices of order 3 $$ \times $$ 3. If det(ABA^T) = 8 and det(AB^–1) = 8,
then det (BA^–1 B^T) is equal to :

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 one solution, then :