Math/Comp 128
Take-home Exam 1
Fall 2005
Instructions: The instructor is the only person you may consult with in
working on this exam. You may use your textbook, homework, calculator, and
class notes,
Math/Comp 128, Homework 2
Due Sept. 22, 2005
1. Text, 2.1
2. Text, 2.2, part a only
3. Text, 4.1b,c,e
4. Text, 4.3 (this is a Matlab assignment). (You only need to apply your algorithm to matrices
in
Math/Comp 128 Homework 3
Due Sept. 29, 2005
1. Let Q be an n n unitary matrix. Show that Q
2
= 1 and Q
F
=
n.
2. Show that the product of two unitary matrices is unitary.
3. Let A be m n with m > n an
Math/Comp 128
Homework 4
Due Oct. 6, 2005
1. Number 6.1 in text (pg. 47)
2. Number 6.4 in text (pg. 47)
3. Number 7.1a in text
4. Repeat exercise 3 on Homework 3 but using the reduced QR factorization
Math 250NLA
Take-home Exam 1
Fall 2005
Instructions: The instructor is the only person you may consult with in
working on this exam. You may use your textbook, homework, calculator, and
class notes, a
Math 128/ Comp 128
EXAM 2
Spring 2004
INSTRUCTIONS: Write all your answers in your blue book. Cross out anything you do not
want graded. No notes or textbooks are allowed. Calculators are permitted as
Solutions for Homework Assignment 8
Math/Comp 128
23.1. We have that A is a nonsingular square matrix with its QR factorization
A = QR. Therefore, we have that A A = R Q QR = R R. Since A A is
hermiti
Solutions for Homework Assignment 7
Math/Comp 128
3 2 17
1. We want to compute the LU factorization of the matrix A = 3 2 1.
1 1
1
3 2
17
1
00
4
18 .
First, we dene L1 = 1 1 0 and compute L1 A = U1 =
Solutions for Homework Assignment 6
Math/Comp 128 - Math 250NLA
1. Let A = U V be the SVD of A. We want to nd the solution to the least
squares problem
minx Ax b 2 ,
with the smallest 2-norm. Using th
Solutions for Homework Assignment 4
Math/Comp 128
1. Since P is an orthogonal projector, we know that P = P 2 and P = P . We
want to show that I 2P is unitary. It is enough to show that (I 2P ) (I 2P
Solutions for Homework Assignment 2
Math/Comp 128
1. The 2-norm and the Frobenius norm are invariant under unitary multiplication, that is, if Q is unitary, then QA 2 = A 2 and QA F = A F for
any matr
Solutions for Homework Assignment 2
Math/Comp 128
1. Assume the matrix A is upper triangular. Then its inverse, A1 , is upper
triangular. On the other hand, its adjoint matrix, A , is lower triangular
Homework Assignment 1
Math/Comp 128
Due Sept. 15, 2005
1. Does the matrix
21
A= 4 2
1 1
satisfy the denition of a full-rank matrix? Justify your answer.
2. Text, 1.1, part a. The idea is that each st