Consider the set defined by the following inequalities

1. Draw the set. Is it convex?

2. Show that it can be described as a single quadratic inequality of the form q(x) = x^T Ax + 2b^Tx + c ≤ 0, for matrix A = A^T ∈ R^2,2, b ∈ R² and c ∈ R which you will determine.

3. What is the convex hull of this set?

(x2x2-1 and x2 > 0) or (x1 x2-1 and x2 0).