Recent content by rolltide2014

As a proof, could I just use some arbitrary third degree polynomial like Hallsofivy did earlier, and plug the numbers into that? Or am I totally headed in the wrong direction with that idea?

I really am just having a hard time figuring out where to begin showing these proofs. I know everything I need is obviously given, but without an equation or something to plug numbers into, I can't figure out where to start. This whole concept is just hard for me to wrap my brain around I guess.

Okay, that's what i thought but just wanted to make sure. So for proving that it is a linear transformation would it be something like: [p(3),p'(1),integral of p(x)] + [q(3),q'(1),integral of q(x)] = [p+q(3),(p+q)'(1),integral of p+ q(x)] That just doesn't like right to me at all, so am I...

Please forgive me if I'm asking a stupid question here, but where did you come up with that equation for p(x)? Or was that just an example?

Well I guess I'm just missing something here or overanalyzing it perhaps. The way T(p) is written with the three terms: the p(3) and then its derivative and integral is throwing me off I think. I haven't seen it written like that before. It was assigned as a take home problem and the professor...

I know in order to be a linear transformation, the following must be true: f(u + v)=F(u) + f(v) and f(cv)=cf(v) I believe. I guess I don't understand the notation and what I am supposed to be proving. Am i supposed to be proving how both the derivative and the integral are linear...

Homework Statement Define a function T: Psub3-->R3 by: T(p)=[p(3),p'(1), integral from 0 to 1 of p(x)dx] for p a polynomial in P sub3, the polynomials of degree less than or equal to 3. a. Show that T is a linear transformation b. Identify Psub3 with R4 in the usual way and write T...