# Polynomials in a subspace

Give an example of a four-dimensional subspace of $P_4$ which contains the polynomials $3 + 2t^2 - 6t^4$ and $1 - 2t + 3t^3$.

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This problem is really quite simple. Take Zev's hint. What does $P_4$ look like? What is its dimension? What does it mean for a subspace to contain those polynomials? –  Lepidopterist Apr 8 '13 at 3:19
I just have a crappy professor who teaches theories and not application. I understand the concept of a subspace and polynomials. I believe we will get a 5 x 3 matrix as a result of this to show that the vectors are independent and form a basis. I just dont understand how to get the actual numbers. –  D-Man Apr 8 '13 at 3:22
@D-Man: Given that this is an entirely theoretical question, I don't see how that aspect of your professor's teaching style is relevant. –  Zev Chonoles Apr 8 '13 at 3:32
Seriously man? haha. lets not try to act like this is some sophisticated website where harvard grads come to answer questions. Your insignificant to me so I dont really care about your opinion. I just need help. If you dont want to give it move on. and the question has a physical answer that I know I just dont know how to get to that answer. So it isint just theoretical. obviously my professors teaching style has nothing to do with this. thanks for that insight Zev. –  D-Man Apr 9 '13 at 4:06

(2) Take your vectors' span: now they're contained in a 2-dimensional subspace of $\,P_4\,$