For a, b ∈ ℝ, let
p(x, y) = a2x1y1 + abx2y1 + abx1y2 + b2x2y2,
x = (x1, x2), y = (y1, y2) ∈ ℝ2. For what values of a and b does
p : ℝ2 × ℝ2 → ℝ define an inner product?
1
a > 0, b > 0
2
ab > 0
3
a = 0, b = 0
4
For no values of a, b
5
Question Not Attempted