Math 118, Spring 2009, Wilkening
Homework 2
due Thurs., Feb. 5
(1) Let Abe an m×nmatrix. Prove that
kAk∞= max
1≤i≤m
n
X
j=1
|Aij|.
(2) Let a≤x0≤band consider the linear functional `:C[a, b]→Cdefined via
`(f) = f(x0).
Show that k`k= 1 when C[a, b] is given the max norm kfk∞= maxa≤x≤b|f(x)|.
(3) problem 19 page 35
(4) problem 21 page 35
(5) problem 28 page 36. It appears that pages 36-37 are missing in the reader.
Problem 28 asks you to find the best fit least squares parabola for the following data:
x0 1 3 4
y08820