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## Homework Statement

Define a Function T : P

_{3}→ ℝ

^{3}by

T(p) = [p(3), p'(1),

_{0}∫

^{1}p(x) dx ]

Show that T is a linear transformation

## Homework Equations

From the definition of a linear transformation:

f(v

_{1}+ v

_{2}) = f(v

_{1}) + f(v

_{2})

and

f(cv) = cf(v)

## The Attempt at a Solution

This is how I've started the problem, but I'm not sure I'm heading in the right direction. Either way I'm stuck.

T(p+q) = (p+q)(3), (p+q)'(1), ∫(p+q)(x)dx

= p(3) + q(3), p'(1) + q'(1), ∫p(x)dx + ∫q(x)dx

I'm not sure where to go from here. Thanks