Let A be a 2 $$ \times $$ 2 real matrix with entries from {0, 1} and |A| $$ \ne $$ 0. Consider the following two statements :

(P) If A $$ \ne $$ I₂ , then |A| = –1
(Q) If |A| = 1, then tr(A) = 2,

where I₂ denotes 2 $$ \times $$ 2 identity matrix and tr(A) denotes the sum of the diagonal entries of A. Then :

Let S be the set of all $$\lambda $$ $$ \in $$ R for which the system of linear equations

2x – y + 2z = 2
x – 2y + $$\lambda $$z = –4
x + $$\lambda $$y + z = 4

has no solution. Then the set S :

The following system of linear equations
7x + 6y – 2z = 0
3x + 4y + 2z = 0
x – 2y – 6z = 0, has

If for some $$\alpha $$ and $$\beta $$ in R, the intersection of the following three places
x + 4y – 2z = 1
x + 7y – 5z = b
x + 5y + $$\alpha $$z = 5
is a line in R³, then $$\alpha $$ + $$\beta $$ is equal to :