Question

Linear Algebra: How do you know whether or not a function is in a certain subspace?
for example:
show Q={p(t)=a+b(1-t^2)+c(1-2t+t^4):a,b,c epsilon R} is a subspace of (PI)4

Answer 1

I don't know what you mean by (PI)4, but I do know that if you want to test for a subspace, you have to show that
(1) Q is a subset of (PI)4
(2) If p and q are elements of Q, then p+q is in Q
(3) If c is any scalar and p any vector in Q, then cp is in Q too.