Question

Linear Algebra: Is P={p(x) in P2: p(x)=p(-x)} a subspace of P2? Please explain.

Answer 1

\(P_2\) is polynomials of degree 2?

Answer 2

if so i think the answer would be yes, but you have to check
is it closed under addition? yes because this means the polynomial is even and must look like
\(a_2x^2+a_1\)

Answer 3

the zero polynomial is in there
and it is also closed under scaler multiples
i don't see any problem but you should check against all conditions (axioms)