MATH 580: Problem Set 1 due Tuesday, September 14, 2004
1. Are y 2 and y 4 linearly independent? Why or why not? 2. Keener 1.1.3a (p.49) 3. Keener 1.1.5 (p.49) 4. Keener 1.1.8 (p.49) 5. Why isn't |x| x, x a valid induced norm? 6. Let f1 , f2 , f3 ,
MATH 580 - Fall 2004 Introduction to Applied Mathematics I
Andrew Belmonte
Time: TR 9:45 - 11:00 AM Location: 018 Henderson Bldg (Tues) & 221 Hammond Bldg (Thurs) - to be changed! Schedule Number: 338641 This graduate course covers some of the techni
MATH 580: Problem Set 5 due Tuesday, October 19, 2004
1. Given two arbitrary vectors U = (u1 , u2 ) and V = (v1 , v2 ) from a linear vector space S, show that U, V = (u1 u2 ) 2 1 1 3 v1 v2
defines a valid inner product on S. Note that you will need
MATH 580: Problem Set 4 due Tuesday, October 12, 2004
1. For what values of b does the equation Ax = b have a solution, given that 3 -1 1 A= 1 -1 3 2. Find the pseudoinverse of M= 3. Consider the matrix C= 3 a 2 1 4 -2 . i 1 -1 i
For what values
MATH 580: Review of Matrices Fall 2004
Given B, a m n (rows by columns) matrix: 1. B T B is square and symmetric 2. if B has linearly independent columns (i.e. B has rank n, assuming n < m) then B T B is symmetric positive definite, which means that
MATH 580: Problem Set 6 due Tuesday, October 26, 2004
1 1 1 1 1. Find the norms of the vectors u = (1, 2 , 1 , 1 , 16 , .) and v = (1, 3 , 1 , 27 , .) 4 8 9 in the Hilbert space 2 using the Euclidean inner product, and verify explicitly the Schwartz
MATH 580: Problem Set 2 due Thursday, September 23, 2004
1. Show that the following are or are not linear vector spaces, and provide a basis set for each if appropriate: a) the set of all symmetric 3 x 3 matrices; b) the set of all 4th order polynom
MATH 580: Problem Set 3 due Thursday, September 30, 2004
1. Are the following matrices invertible? If so, calculate the inverse. B= i 1 -1 i ; P = 3 a 1 4
(for P , specify for which values of a the inverse P -1 exists). 2. Consider the matrix A= 4