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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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Since you are new, I want to give some advice about the site: To get the best possible answers, you should explain what your thoughts on the problem are so far. That way, people won't tell you things you already know, and they can write answers at an appropriate level; also, people tend to be more willing to help you if you show that you've tried the problem yourself. If this is homework, please add the [homework] tag; people will still help, so don't worry. Also, some would consider your post rude because it is a command ("Give"), not a request for help, so please consider rewriting it. –  Zev Chonoles Apr 8 '13 at 3:14
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

1 Answer 1

Some ideas:

(1) Check that both your polynomials (vectors) are linearly independent

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

(3) If you really need 4th dimensional subspace, just add two polynomials (vectors) to your given two that are lin. independent from them...

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