Question

Solve the problem. Determine which of the following sets is a subspace of Pn for an appropriate value of n. A: All polynomials of the form p(t) = a + bt2, where a and b are in ℛ B: All polynomials of degree exactly 4, with real coefficients C: All polynomials of degree at most 4, with positive coefficients

Answer 1

Only $A$ and $B$ form subspaces of $P_2$ and $P_4$, respectively.

$C$ does not form a subspace because it does not contain the zero vector.