Question

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

Answer 1

@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?

Answer 2

yes, I think so.

Answer 3

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?

Answer 4

Yeah, that's what I was thinking.

Answer 5

It would only work for \(n<2\).

Answer 6

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?

Answer 7

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

Answer 8

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

Answer 9

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