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## Homework Statement

V = {p(x) belongs to P3 such that p'(1) + p'(-1) = 0}

## Homework Equations

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## The Attempt at a Solution

Okay, so finding the first derivative of p(x) = ax^3 + bx^2 + cx + d and plugging in the values 1 and -1 (to find p'(1) and p'(-1)), we get c = -3a. Does this make the basis of V = {x^3 - 3x, x^2, 1}. And the dimension hence is 3? I'm fairly new to the subject.

Also, when wanting to prove a transformation is one-to-one, does finding that the nullspace of T = {0} (i.e, the homogenous system has only one trivial solution which is 0) suffice?

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