- #1
Inirit
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Homework Statement
Which of these subsets of P2 are subspaces of P2? Find a basis for those that are subspaces.
(Only one part)
{p(t): p(0) = 2}
Homework Equations
The Attempt at a Solution
So, I know the answer is that it's not a subspace via back of the book, but I don't understand why. Supposedly it's because it doesn't contain p(t) = 0 for all t, but I don't see why that's true. If p(0) = 2, then the equation has to look like 2 + bt + ct^2. If b,c = -1, then p(1) = 0, therefore there is a way for p(t) = 0.
Maybe I am just not understanding something. Admittedly, I feel really lost with all this.