## Matrices and Linear Operatos 1;

PITT Math 2370, Fall 2017

# Homeworks

Homework 1
Due Wednesday Sept 6 in class:

From the textbook (Linear Algebra, by Hoffman and Kunze, 2nd Edition)

Problem 1.    Section 1.2, Exercise 1.
Problem 2.    Section 1.2, Exercise 6.
Problem 3.    Section 1.3, Exercise 4.
Problem 4.    Section 1.3, Exercise 8.
Problem 5.    Section 1.4, Exercise 8.
Problem 6.    Section 1.4, Exercise 10.
Problem 7.    Section 1.5, Exercise 3.
Problem 8.    Section 1.5, Exercise 8.

Homework 2
Due Wednesday Sept 13 in class:

From the textbook (Linear Algebra, by Hoffman and Kunze, 2nd Edition)

Problem 1.    Section 1.6, Exercise 7.
Problem 2.    Section 1.6, Exercise 10.
Problem 3.    Section 2.1, Exercise 3.
Problem 4.    Section 2.1, Exercise 4.
Problem 5.    Section 2.1, Exercise 7.
Problem 6.    Section 2.2, Exercises 1 (d) (e) and and 2 (a) (d).
Problem 7.    Section 2.2, Exercise 3.
Problem 8.    Section 2.2, Exercise 6.
Problem 9.    Section 2.2, Exercise 7.
Problem 10.  Section 2.2, Exercise 9.

Homework 3
Due Wednesday Sept 20 in class:

From the textbook (Linear Algebra, by Hoffman and Kunze, 2nd Edition)

Problem 1.    Section 2.3, Exercise 5.
Problem 2.    Section 2.3, Exercise 6.
Problem 3.    Section 2.3, Exercise 7.
Problem 4.    Section 2.3, Exercise 14.
Problem 5.    Section 2.4, Exercise 2.
Problem 6.    Section 2.4, Exercise 7.
Problem 7.    Section 2.6, Exercise 1.
Problem 8.    Section 2.6, Exercise 3.
Problem 9.    Section 2.6, Exercise 6.
Problem 10.  Section 2.6, Exercise 7.

Homework 4
Due Wednesday Sept 27 in class:

From the textbook (Linear Algebra, by Hoffman and Kunze, 2nd Edition)

Problem 1.    Section 3.1, Exercise 3.
Problem 2.    Section 3.1, Exercise 9.
Problem 3.    Section 3.1, Exercise 10.
Problem 4.    Section 3.1, Exercise 12.
Problem 5.    Section 3.2, Exercise 6.
Problem 6.    Section 3.2, Exercise 8.
Problem 7.    Section 3.2, Exercise 10.
Problem 8.    Section 3.2, Exercise 11.

Homework 5
Due Wednesday Oct 4 in class:

From the textbook (Linear Algebra, by Hoffman and Kunze, 2nd Edition)

Problem 1.    Section 3.3, Exercise 4.
Problem 2.    Section 3.3, Exercise 5.
Problem 3.    Section 3.3, Exercise 7.
Problem 4.    Section 3.4, Exercise 2.
Problem 5.    Section 3.4, Exercise 5.
Problem 6.    Section 3.4, Exercise 8.
Problem 7.    Section 3.4, Exercise 12.
Problem 8.    Section 3.5, Exercises 2 and 4.
Problem 9.    Section 3.5, Exercises 3 and 5.
Problem 10.  Section 3.5, Exercise 11.

Homework 6
Due Wednesday Oct 11 in class:

From the textbook (Linear Algebra, by Hoffman and Kunze, 2nd Edition)

Problem 1.    Section 3.5, Exercise 14.
Problem 2.    Section 3.5, Exercise 16.
Problem 3.    Section 3.5, Exercise 17.
Problem 4.    Section 3.6, Exercise 3.
Problem 5.    Section 3.7, Exercise 3.
Problem 6.    Section 3.7, Exercise 7.
Problem 7.    Section 3.7, Exercise 8.

From Linear Algebra Prelim Sample Exams

Problem 8.    April 2015, Problem 4
Problem 9.    April 2015, Problem 5 (a) and (b). Also write the matrix of the operator ad in a basis of sl(2,C) of your choice.
Problem 10.  August 2014, Problem 6
Problem 11.  April 2014, Problem 1 (Bonus problem, 2/10 extra HW points)
Problem 12.  August 2013, Problem 3 (Bonus problem, 2/10 extra HW points)

Homework 7
Due Wednesday Oct. 25 in class:

From the textbook (Linear Algebra, by Hoffman and Kunze, 2nd Edition)

Problem 1.    Section 4.2, Exercises 1 and 2.
Problem 2.    Section 4.2, Exercise 4.
Problem 3.    Section 4.2, Exercise 6.
Problem 4.    Section 4.3, Exercise 2.
Problem 5.    Section 4.3, Exercises 3 and 4.
Problem 6.    Section 4.3, Exercise 6.
Problem 7.    Section 4.4, Exercise 2(b).
Problem 8.    Section 4.4, Exercise 4.
Problem 9.    Section 4.4, Exercise 6.
Problem 10.  Section 4.4, Exercise 7.

Homework 8
Due Wednesday Nov. 1 in class:

From the textbook (Linear Algebra, by Hoffman and Kunze, 2nd Edition)

Problem 1.    Section 5.2, Exercise 5.
Problem 2.    Section 5.2, Exercise 8.
Problem 3.    Section 5.2, Exercise 10.
Problem 4.    Section 5.2, Exercise 12.
Problem 5.    Section 5.2, Exercise 14.
Problem 6.    Section 5.3, Exercise 2.
Problem 7.    Section 5.3, Exercise 7.
Problem 8.    Section 5.3, Exercise 10.
Problem 9.    Section 5.3, Exercise 11.
Problem 10.  Section 5.3, Exercise 12.

Homework 9
Due Wednesday Nov. 8 in class:

From the textbook (Linear Algebra, by Hoffman and Kunze, 2nd Edition)

Problem 1.    Section 5.4, Exercise 3.
Problem 2.    Section 5.4, Exercises 4 and 5.
Problem 3.    Section 5.4, Exercise 6
Problem 4.    Section 5.4, Exercise 8.
Problem 5.    Section 5.4, Exercise 9.
Problem 6.    Section 5.4, Exercise 11.
Problem 7.    Section 5.4, Exercise 12.
Problem 8.    Section 5.4, Exercise 14

Homework 10
Due Wednesday Nov. 15 in class:

From the textbook (Linear Algebra, by Hoffman and Kunze, 2nd Edition)

Problem 1.    Section 6.2, Exercise 2. (Write the complete formal proof).
Problem 2.    Section 6.2, Exercise 3.
Problem 3.    Section 6.2, Exercises 4 and 5.
Problem 4.    Section 6.2, Exercises 8 and 9.
Problem 5.    Section 6.2, Exercise 13.
Problem 6.    Section 6.3, Exercises 1 and 3.
Problem 7.    Section 6.3, Exercises 5 and 6.
Problem 8.    Section 6.3, Exercise 7.

Homework 11
Due Friday Dec. 1 in class:

From the textbook (Linear Algebra, by Hoffman and Kunze, 2nd Edition)

Problem 1.    Section 6.4, Exercise 2.
Problem 2.    Section 6.4, Exercise 5.
Problem 3.    Section 6.4, Exercise 6.
Problem 4.    Section 6.4, Exercise 8.
Problem 5.    Section 6.4, Exercise 10.
Problem 6.    Section 6.4, Exercise 12.
Problem 7.    Section 6.5, Exercises 1 and 2.
Problem 8.    Section 6.5, Exercise 3.
Problem 9.    Section 6.6, Exercise 2.
Problem 10.  Section 6.6, Exercise 6.

Homework 12
Due Friday Dec. 15 at noon:

From the textbook (Linear Algebra, by Hoffman and Kunze, 2nd Edition)

Problem 1.    Section 6.6, Exercise 8.
Problem 2.    Section 6.6, Exercise 9.
Problem 3.    Section 6.7, Exercise 3.
Problem 4.    Section 6.7, Exercise 4.
Problem 5.    Section 6.7, Exercise 6.
Problem 6.    Section 6.8, Exercise 3.
Problem 7.    Section 6.8, Exercise 4.
Problem 8.    Section 6.8, Exercise 5.
Problem 9.    Section 6.8, Exercise 6.
Problem 10.  Section 6.8, Exercise 8.