Which of the following subsets of P2 are subspaces of P2 A p

Which of the following subsets of P_2 are subspaces of P_2? A. {p(t) |p(8) = 8} B. {p(t) | p(-t) = p(t) for ail t} C. {p(t) | p\'(t) + 6p(t) + 7 = 0} D. {p(t) |p\'(1) = p(7)} E. {p(t) | integral_0^3 p{(t)dt = 0} F.{p(t) |p(0) = 0}

Solution

B, C, E, F are subspaces. You need to check whether they contain 0 and are closed under addition and scalar multiplication. Keep in mind that the derivative and integral are linear.