
MAT 211: Homeworks
Homework is a compulsory part of the course. Homework assignments are due each week at the beginning of the Wednesday class (9:10am).
Under no circumstances will late homework be accepted.
You are encouraged to discuss homework with other students in 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 
W 2/4 
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 
W 2/11 
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 
W 2/18 
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 
W 2/24 
3^{rd} ed. Sec. 2.4: 1, 3, 11, 12, 13, 26, 36, 41, 43, 76
4^{th} ed. Sec. 2.3: 1, 3, 11, 12, 13, 16, 20, 29, 45, 55 
Practice matrix multiplication, and think about what it means. 
HW 5 
W 3/4 
3^{rd} ed. Sec. 2.3: 4, 6, 16, 17, 30
4^{th}ed. Sec. 2.4: 4, 6, 16, 17, 30 3^{rd} and
4^{th}: 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. 
HW 6 
W 3/11 
Sec. 3.1: 2, 3, 6, 16, 23, 24, 25
Sec. 3.2: 28, 32 Sec. 3.3: 22, 24, 31, 36, 38

You are also responsible for parts of HW 5 that you have not yet submitted.
In preparation for the exam, read thru section 3.1
(and then 3.2 and 3.3). It will be a good review
of everything. We will discuss Ker and Im in class on Monday.

HW 7 
W 3/25 
Sec. 3.3: 23, 81 Sec. 3.4: 22, 38, 55, 58, 62 Sec. 4.1: 1, 22, 25, 26, 30

Revisit Kernel and Image, especially the Rank Nullity Theorem. Try on different bases. The change
of basis matrix may help. Get used to
new vector spaces. 
HW 8 
We 4/1 
Sec. 3.4: 30, 42, 53, 56, 75 Sec. 4.1: 4, 23,
28 
This is the second episode of HW 7, for extra practice
with this difficult material 
HW 9 
W 4/15 
Sec. 4.2: 3, 6, 52, 30, 56 Sec. 4.3: 6, 22, 28
Sec. 5.1: 6, 10, 17

Linear transformations of vector spaces and their matrices in different bases. Euclidean spaces. 
HW 10 
W 4/21 
Sec. 5.1: 16, 26, 29 Sec. 5.2: 4, 29, 32 Sec. 5.5: 14 
These are is exercises for Midterm 2. Learn how to work in inner product spaces. 
HW 11 
W 4/29 
Sec. 6.1: 6, 8, 18 Sec. 6.2: 6, 14, 48

Go determinants! 
HW 12 
Tu 5/5 
Sec. 6.3: 1, 2 Sec. 7.1: 1, 10 Sec. 7.2: 4
Sec. 7.3: 2, 10 Sec. 7.4: 4, 6

Eigenvalues and eigenvectors. Study diagonalization. 
