## Introduction to Linear Algebra

### MAT 211 (LEC 3)

#### Spring 2009

Mathematics department
Julia Viro

Generalities Instructors Schedule Homework Exams Help

## Homework

Homework is a compulsory part of the course. Homework assignments are due each week at the beginning of the Tuesday's class (12:50pm). Under no circumstances will late homework be accepted.

You are encouraged to study together with other students in the class, however the work you hand in should be your own, not copied from someone else. No credit will be given to solutions with suspiciously identical mistakes.

HW Due date Assignment Remarks
HW 1 Tu 2/3 Sec.1.1: 2, 6, 10, 12, 26, 29
Sec.1.2: 8, 10, 18, 46
Solutions of linear systems are easy to check. Don't miss this opportunity!
HW 2 Tu 2/10 Sec.1.3: 2, 3, 4, 16, 17, 18, 19, 36, 47, 60 Matrix multiplication is one of the most important operations for us. Exercise!
HW 3 Tu 2/17 Sec. 2.1: 1, 2, 3, 4
Sec. 2.2: 6, 7, 20, 40, 41, 42
Make sure that you understand the nature of a linear transformation.
HW 4 Tu 2/24 3rd ed. Sec. 2.4: 1, 3, 11, 12, 13, 26, 36, 41, 43, 76
4th ed. Sec. 2.3: 1, 3, 11, 12, 13, 16, 20, 29, 45, 55
Multiply matrices
HW 5 Tu 3/3 3rd ed. Sec. 2.3: 4, 6, 16, 17, 30
4thed. Sec. 2.4: 4, 6, 16, 17, 30
3rd and 4th: Sec. 3.2: 6, 9, 18; Sec. 3.3: 28, 30 Sec. 3.4: 16, 18
Learn how to invert 2x2 and 3x3 matrices (when possible). Verify the result. How to test linear dependence/independence? What is a basis and how to find it? Get used to coordinates.
We are close to Midterm 1, so the assignments are getting longer.
HW 6 Tu 3/10 Sec. 3.1: 2, 3, 6, 16, 23, 24, 25
Sec. 3.2: 28, 32
Sec. 3.3: 22, 24, 31, 36, 38
This is an opportunity to exercise for Midterm I, so double your work! Learn how to work with kernel and image of lin. transformations and bases of subspaces. Ker-Im theorem is a must.
HW 7 Tu 3/24 Sec. 3.4: 22, 38, 55, 58, 62
Sec. 4.1: 1, 22, 25, 26, 30
Try on different bases. The change of basis matrix may help. Get used to new vector spaces.
HW 8 Tu 3/31 Sec. 3.4: 30, 42, 53, 56, 75
Sec. 4.1: 4, 23, 28
This is the second episode of HW 7
HW 9 Tu 4/14 Sec. 4.2: 4, 6, 52, 30, 56
Sec. 4.3: 6, 22, 28, 47
Sec. 5.1: 6, 10, 17
Linear transformations of vector spaces and their matrices in different bases. Euclidean spaces.
Tu 4/16 Bonus Test This is an opportunity to practice for Midterm 2
HW 10 Tu 4/21 Sec. 5.1: 26
Sec. 5.2: 4, 29, 32
Sec. 5.3: 34, 40
Sec. 5.5: 10, 20, 22, 23
These are is exercises for Midterm 2. Learn how to work in inner product spaces.
Tu 4/28 No homework
HW 11 Tu 5/5 Sec. 6.1: 6, 8, 18
Sec. 6.2: 6, 22
Sec. 6.3: 2, 3, 24
Sec. 7.3: 1, 2, 10
Sec. 7.4: 4, 6, 49, 50
Go determinants! Meet our new friends: eigenvalues and eigenvectors. Study diagonalization.