In polynomial vector space, is P (ax) = a P(x)?
Please help

Question

In polynomial vector space, is P (ax) = a P(x)? 
Please help

anonymous · Answer

@Loser66, it's been a while since I've had linear algebra, but any element in this vector space would have the form $a_0+a_1x+a2x^2+\cdots+a_nx^n$, correct?

loser66 · Answer

yes, I think so.

loser66 · Answer

I think it is not equal
Let P(x) = x^2 +3
P(2x) = (2x)^2 +3 $\neq$2P(x) = 2x^2 +6
am I right?

anonymous · Answer

Yeah, that's what I was thinking.

anonymous · Answer

It would only work for $n<2$.

loser66 · Answer

but the problem ask me:
Prove that it is a linear transformation: V is P; if x is a polynomial, then (Ax)(t) = x(t+1)-x(t)
Does it imply that  A is a linear transformation?

loser66 · Answer

which is A(aX(t) = aA(X)(t) = aAX(t)

anonymous · Answer

Hmm, I'm not so familiar with any of this notation... Sorry.

loser66 · Answer

It's ok, I am confused everything, hehehe...