Math 235 - Linear Algebra - Fall 2014

Please show all work and explain all reasoning behind your solution. Writing down an answer without an explanation will result in no credit for the problem!

Homework 1, to be handed in 9/4/2014:

Section 1.1: 11, 13, 15, 21

Section 1.2: 1, 3, 11

Section 1.3: 9, 13, 15, 17

There will be a quiz on this material on 9/4/2014.

Homework 2, to be handed in 9/11/2014:

Section 1.4: 12, 17, 19, 22, 26

Section 1.5: 5, 11, 17, 25

Section 1.6: 7

There will be a quiz on this material on 9/11/2014.

Homework 3, to be handed in 9/18/2014:

Section 1.6: 12

Section 1.7: 2, 15, 16, 17, 27, 28

Section 1.8: 4, 7, 19, 24, 30

There will be a quiz on this material on 9/18/2014.

Homework 4, to be handed in 9/25/14:

Section 1.9: 5, 6, 17, 22

Section 2.1: 2, 4, 7, 8, 10, 22

Section 2.2: 2, 7, 19, 31, 33

There will be a quiz on this material on 9/25/14.

Homework 5, to be handed in 10/3/14:

Section 2.3: 4,6,13,14,15,18,28,33

Note: In 28, you may NOT assume that B is invertible! You must show that it has an inverse by using the Invertible Matrix Theorem.

Section 2.4: 5, 10, 25

Section 2.8: 5, 7, 15, 18

Homework 6, to be handed in 10/10/14:

Section 4.1: 1, 2, 5, 7, 11, 12, 13, 20, 21, 22

There will be a quiz on this material on 10/9/14.

Homework 7, to be handed in 10/17/14:

Section 2.9: 9, 10, 11

Section 4.2: 2, 16, 18, 23, 33, 34

Section 4.3: 15, 16, 21, 26

There will be a quiz on this material on 10/17/14.

Homework 8, to be handed in 10/24/14.

Section 4.4: 9, 11, 12, 13, 27, 28, 32

Section 4.5: 4, 5, 7, 12, 13, 14, 21

There will be a quiz on this material on 10/23/14.

Homework 9, to be handed in 10/31/14.

Section 3.1: 1, 3, 9, 14, 16

Section 3.2: 5, 8, 10, 12, 27, 29, 34, 40abc

Section 3.3: 2, 8, 19, 27

Homework 10, the be handed in 11/7/14.

Section 5.1: 6, 7, 9, 13, 17, 18, 24, 25, 26

Section 5.2: 2, 10, 11, 12, 16

For the problems in section 5.2, find all eigenvectors for each eigenvalue also.

There will be a quiz on this material on 11/6/14.

Homework 11, the be handed in 11/17/14.

Section 5.3: 2, 3, 6, 11, 12, 13, 14, 25, 27, 32

Section 5.5: 1, 2, 7, 8, 14

There will not be a quiz on this material this week.

Homework 12, to be handed in 11/21/14

Section 6.1: 2, 4, 6, 13, 16, 22, 24, 30, 31

For problem 16, find the orthogonal complement to the subspace spanned by u and v.

There will be a quiz on 5.3, 5.5, and 6.1 on 11/20/14.

Syllabus (subject to change as the course progresses):

Week 1: 8/25 - 8/29

1.1 Systems of Linear Equations

1.2 Row Reduction and Echelon Forms

1.3 Vector Equations

Week 2: 9/1 - 9/5

1.4 The Matrix Equation Ax=b

1.5 Solution Sets of Linear Systems

1.6 Applications of Linear Systems

Week 3: 9/8 - 9/12

1.7 Linear Independence

1.8 Introduction to Linear Transformations

Week 4: 9/15 - 9/19

1.9 The Matrix of a Linear Transformation

2.1 Matrix Operations

2.2 The Inverse of a Matrix

Week 5: 9/22 - 9/26

2.3 Characterizations of Invertible Matrices

2.4 Partitioned (Block) Matrices

2.8 Subspaces of R^n

Week 6: 9/29 - 10/3

2.9 Dimension and Rank in R^n

4.1 Vector Spaces and Subspaces

MIDTERM 1 WILL BE ON THURSDAY, 10/2/14.

Week 7: 10/6 - 10/10

4.2 Null Spaces, Column Spaces, and Linear Transformations

4.3 Linearly Independent Sets and Bases

4.4 Coordinate Systems

Week 8: 10/15 - 10/16

4.4 Coordinate Systems (continued)

4.5 Dimension of a Vector Space

Week 9: 10/20 - 10/24

3.1 Introduction to Determinants

3.2 Properties of Determinants

3.3 Cramer's Rule

Week 10: 10/27 - 10/31

5.1 Eigenvalues and Eigenvectors

5.2 The Characteristic Equation

MIDTERM 2 IS ON THURSDAY, 10/30/14.

Week 11: 11/3 - 11/7

5.3 Diagonalization

5.5 Complex Eigenvalues

Week 12: 11/10 - 11/14

6.1 Inner Product, Length, and Orthogonality

6.2 Orthogonal Sets

Week 13: 11/17 - 11/21

6.2 Orthogonal Sets

6.3 Orthogonal Projections

Week 14: 11/24 Midterm 3 (tentative)

Week 15: 12/1 - 12/5

6.4 The Gram-Schmidt Process

6.5 Least-Squares