Math 321 Syllabus and Homework Assignments (Prof. Lushnikov), Spring 2026

Column Date below is filled with dates for sections I (Prof. Lushnikov)  finished lecturing on.  DP means D. Poole's book. Homework is due each Tuesday (I pick up homework before lecture start) for all sections assigned from the previous week. For your convenience I also include due date for each homework assignment in column Due date.  I recommend to read sections before I actually lecture on them. You might not understand them well, but you can find out the main concepts and have some questions already in mind when you listen to lectures.  After you turn in assignments, I'll place *'s next to the problems being graded. Currently there are sections listed for all the material I plan to cover in D. Poole's book. However, I might decide to change some of them as the semester progresses, perhaps even adding or deleting a section here and there. So please return to this page periodically to make sure you are working the correct homework problems. Solution will be posted only to problems without answer key in DP.

Solutions of hw 1 

Solutions of hw 2 

Solutions of hw 3

 

Date

Section

Homework

Due date

 

 

 

Hw 1:

 

1

01/20/26

DP 1.1 The geometry and algebra of vectors

DP 1.1: 1(a,d),2(d),3(b),4(a,b),8,10,12,16

01/27/26

2

01/22/26

DP 1.2 Dot product.

DP 1.2: 2,3,5,7,11,14,15,17(b),24,25,30,41,43,51,55,59,66,71(optional)

01/27/26  

 

 

 

 Hw 2:

 

3

01/27/26

DP 1.3 Lines and Planes

DP 1.3: 1,2,4,7,9,11,14,15(a),18(a,b),20,23,25(optional), 28,29,31,35,37,41(optional),42(optional),43(optional)

02/03/26

4

01/29/26

DP 1.3 Lines and Planes;

DP 2.1 Introduction to Systems of Linear Equations

DP 2.2 Direct methods for solving linear systems

DP 2.1: 1,2,3,11,15,16,17, 22, 28

02/03/26 

 

 

  Hw 3:

 

5

02/03/26

DP 2.2 Direct methods for solving linear systems

DP 2.2: 1,2,3,4,9,10,14,17,19, 25,26, 34,35,36,40,45,48

02/10/26 

6

02/05/26

DP 2.3 Spanning sets and linear independence

 DP 2.3: 1,2,3,7

02/10/26 

 

 

 

  Hw 4:

 

7

02/10/26

DP 2.3 Spanning sets and linear independence; DP Appendix C

DP  3.1 Matrix operations

DP 2.3: 9,10,11,12,13(a,b),14(a,b),15(a,b),19,21(optional),22,23,24,43(optional). 25,30,31,34,35,38(optional)

02/17/26

8

02/12/26

DP Appendix C

DP  3.1 Matrix operations

problems 1,2,3,4(a,b,c,d),5 

DP 3.1: 1,2,3,4,5,6,7,8,9,14,13,19,21,23,24 

 02/17/26

 

 

  Hw 5:

 

9

02/17/26

DP  3.1:  Matrix Operations

DP  3.2:  Matrix algebra

DP  3.1:  10,11,12,15,25,30,31,34,35,38(optional)

DP  3.2:  2,6,14,18, 19,20,22,30,33,37(a,b),44,45(optional),46(optional)

02/24/26

10

02/19/26

DP 3.2 Matrix algebra; DP  3.3 Matrix inverse 

DP  3.3: 14,15,16

 02/24/26

 

 

  Hw 6:

 

11

02/24/26

DP  3.3 Matrix inverse; 3.4 LU factorization 

DP  3.3: 2,3,12,13,14,15,17(a),22,24,36,38,40,41,54,57

DP 3.4: 2,3,8,10,19

 03/10/26

12

02/26/26

Review  and DP 3.4 LU factorization 

DP 3.4: 2,3,8,10,19

 

 

 

 

 

13

03/03/26

Test 1 in Class. No hw due on  03/03/26

 

 

14

03/05/26

DP 3.4 LU factorization; DP 6.1 Vector spaces and subspaces

DP 6.1: 1,2,5,7,9,12,14,23,24,27,29(optional) ,34,37 

 03/10/26

 

 

 

   Hw 7:

 

15

03/10/26

DP 6.1 Vector spaces and subspaces; 

DP 3.5 Subspaces, basis, dimension, and rank (p.191)

DP 6.1: 35

 DP 3.5: 2,7,11,12,16

 03/24/26

16

03/12/26

DP 6.2 Linear independence, basis and dimension; 

DP 3.5 Subspaces, basis, dimension, and rank

DP 6.2: 1,5,6,17(optional),18,22,34,40(optional)

DP 3.5: 17,18,19

 03/24/26

 

 

 

 

  

17

03/17/26

Spring break 

 

 

18

03/19/26

Spring break 

 

 

 

 

 

  Hw 8:

 

19

03/24/26

DP 6.2 Linear independence, basis and dimension; 

DP 3.5 Subspaces, basis, dimension, and rank

 

03/31/26 

20

03/26/26

DP 3.5 Subspaces, basis, dimension, and rank; DP 6.2 Linear independence, basis and dimension ; DP 6.3 Change of basis

 

 

03/31/26

 

 

 

  Hw 9:

 

21

03/31/26

DP 6.3 Change of basis

 

 04/14/26

22

04/02/26

 Review and DP 3.6 Introduction to linear transformations; DP 6.4 Linear transformations; 

 

04/14/26 

 

 

 

 

 

23

04/07/26

DP 6.4 Linear transformations; DP 6.5 Kernel and range of linear transformation 

No hw due on  04/07/26

 

 04/14/26 

24

04/09/26

Test 2 in Class.

 

 

 

 

  Hw 10:

 

25

04/14/26

DP 6.5 Kernel and range of linear transformation 

 

04/21/26 

26

04/16/26

DP 6.6. Matrix of linear transfromation..DP 4.2 Determinants; 

 

04/21/26 

 

 

 

  Hw 11:

 

27

04/21/26

DP 4.2 Determinants

 

04/28/26 

28

04/23/26

DP 4.2 Determinants (continue); DP 4.1 Introduction to eigenvectors and eigenvalues; DP 4.3 Eigenvalues of n x n matrices; 

 

04/28/26

 

 

 

  Hw 12:

 

29

04/28/26

P 4.1 Introduction to eigenvectors and eigenvalues; DP 4.3 Eigenvalues of n x n matrices (continue);  DP 4.4 Similarity and diagonalization

 

05/05/26 

30

04/30/26

DP 4.4 Similarity and diagonalization; DP 5.1 Orthogonality; DP 5.2 Orthogonal complements and orthogonal projection   

 

05/05/26 

 

 

 

 

 

31

05/05/26

DP 5.2 Orthogonal complements and orthogonal projection; DP 5.3 Gram-Schmidt orthogonalization. DP  7.1 Inner product spaces

 

 

32

05/07/26

Review

 

  

 

 

 

  

  

 

 

FINAL EXAM TBA