Posted: December 6th, 2015

tennessee state university
college of science and mathematics
Department of Mathematical Sciences
Homework 05 – Math 3610 Fall 2015
Name:
Partial credit will be given. Your job is not only to answer the questions but instead your job is to
show how to obtain the correct answer.
1. Let W := {f : (0, ∞) → R : f is differentiable} over the field F = R. If (f ⊕ g)(x) := f(x) + g(x)
and (α ⊙ f)(x) := α · f(x), then show that (W, ⊕, ⊙) is a vector space.
2. Let V } be the set of all polynomials of degree less of equal to 2 with real coefficients over the field
F = R. If
ax2+bx+c⊕dx2+ex+f := (a+d)x2+(b+e)x+(c+f) and α⊙(ax2+bx+c) := αax2+αbx+αc,
then show that (V, ⊕, ⊙) is a vector space.
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