If the system of equations
x - 2y + 3z = 9
2x + y + z = b
x - 7y + az = 24,
has infinitely many solutions, then a - b is equal to.........

Let S be the set of all integer solutions, (x, y, z), of the system of equations
x – 2y + 5z = 0
–2x + 4y + z = 0
–7x + 14y + 9z = 0
such that 15 $$ \le $$ x² + y² + z² $$ \le $$ 150. Then, the number of elements in the set S is equal to ______ .

Let A = $$\left[ {\matrix{ x & 1 \cr 1 & 0 \cr } } \right]$$, x $$ \in $$ R and A⁴ = [a_ij].
If a₁₁ = 109, then a₂₂ is equal to _______ .

The number of all 3 × 3 matrices A, with enteries from the set {–1, 0, 1} such that the sum of the diagonal elements of AA^T is 3, is