Thread: Subsets that are subspaces of P2

Hello, i recently took a linear algebra test and there was a bonus on it. The bonus was the material that we are going to soon be learning. I have not read ahead so i didnt get it right. I was wondering if you guys could explain it to me.

Bonus:
Which of the following subsets of P2 are subspaces of P2?

A.) p(t)| p'(t)+2p(t)+7=0
B.) p(t)| p(8)=0
C.) p(t)| integral from 0-1(p(t)dt)=0
D.) p(t)| p(7)=4
E.) p(t)| p'(4)=p(0)
F.) p(t)| p(-t)=p(t) for all t


Thank You,
Diggidy

B, C, E, and 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.