Prove that the set S is a subspace of the vector space V v=P^5 and S is the set of polynomials of the form p(x)= a4x^4+a2x^2+a0.

Prove that the set S is a subspace of the vector space V

v=P^5 and S is the set of polynomials of the form p(x)= a4x^4+a2x^2+a0

Solution: 1) For a4 = a2=a0 = 0, we have that the zero polynomial belongs to S.2) Let a4 x^4+ a2 x^2+ a0, b4 x^4+ b2 x^2+ b0 belong to S, then(a4 x^4+ a2 x^2+ a0) + (b4 x^4+ b2 x^2+ b0)…