7 5 pts Determine whether the set of all polynomials a0 a1x

7. (5 pts) Determine whether the set of all polynomials a0 + a1x + a2x^2 for which either a1 = 0 or a2 = 0, a subspace of P2. Must give your reasoning.

Solution

it is NOT a subspace;

let the given set be V

let v1 = x^2 and v2 = x

v1,v2 both belong to V

v1+v2 = x^2 +x, which doesnt belong to V

=>

V is NOT a subspace