Determinants

Let R2 denote R R. Let S= \(a,b,c) : a,b,c R and ax2+2bxy+cy2>0 for all (x,y) R2-\(0,0)\ \. Then which of the following statements is (are) TRUE?

1. (2, 72,6 ) S
2. If (3,b, 112 ) S, then |2b|<1.
3. For any given (a,b,c) S, the system of linear equations ax+by=1 bx+cy=-1 has a unique solution.
4. For any given (a,b,c) S, the system of linear equations (a+1)x+by=0 bx+(c+1)y=0 has a unique solution.

Let S= \A= pmatrix 0 & 1 & c \ 1 & a & d \ 1 & b & e pmatrix : a,b,c,d,e \0,1\ and |A| \-1,1\ \, where |A| denotes the determinant of A. Then the number of elements in S is .