Scientific Computing Using Python - PHYS:4905 - Fall 2018
Homework #8
Due 9/25/2018
Name _______________________________________________
The answers to these questions must be hand written on paper.
1. (12) Show that the pair of conditions:
[1] L(u + v) = L(u)
+ L(v) and L(cv) = cL(v)
which is valid for all vectors u, v and any scalar c,
is equivalent to the single condition:
[2] L(ru + sv) = rL(u)
+ sL(v)
which is valid for all vectors u, v and any scalars
r and s.
Your answer should have two parts. Show that [1] implies [2], and
then show that [2] implies [1].
2. (6) If Q(x2) = x3 and Q(2x2)
= x4 is it possible that Q is a linear
function from polynomials to polynomials? Explain your
reasoning.
3. (20) If f is a linear function such that
and
, then what is
?