f19_math221

Introduction to Linear Algebra

- Fall 2019 -

Instructor: Kwangho Choiy

• Office: Neckers 283 (618-453-6508)

• E-mail: kchoiy_at_siu_dot_edu 

• Office Hours: MWF 9-10am; 12-1pm, or by appointment. Emails are also available for simple questions.

Course Website: https://sites.google.com/site/kchoiy/teaching/f19_math221

Class Meeting: MWF 10:00am - 10:50am in EGRA 220

Textbook: Elementary Linear Algebra 11th edition by Howard Anton.   

Syllabus / Course Schedule: It is required to read carefully our syllabus and schedule linked [here], UPDATED on 8/15/2019.

Exams: There will be three mid-term exams and one final at the classroom EGRA 220. No make-up exam will be accepted.

1.  Exam 1 (in class on 9/6, Fri) covers Sections 1.1-1.3 prac&guideline

2.  Exam 2 (in class on 10/11, Fri) covers Sections 1.4-1.6, 2.1-2.3, 3.1-3.3, 4.1 prac.probl. / guideline

3.  Exam 3 (in class on 11/13, Wed) covers Sections 4.2-4.5, 4.7 prac.probl. / guideline

4.  Final Exam (2:45pm-4:45pm on Dec. 13, FRIDAY, at our classroom) will be comprehensive: approximately, 40% on Sections 1.1--1.6, 2.1--2.3. 3.1--3.3, 4.1--4.5, 4.7 and 60% on Sections 4.8, 5.1-5.2, 1.7, 7.1  prac.probl. / guideline

Each HOMEWORK ASSIGNMENT will be posted as below at least one week ahead of the due date (see the Course Schedule above for a tentative assignment schedule!):

*HW Policies: You should show all your work and submit it in class on the due date. No late homework will be accepted.*

1. HW 1 (due on 8/26, Mon) Sec 1.1: #2, 8, 10, 14, 15, 17, 18, 26

2. HW 2 (due on 9/16, Mon) Sec 1.4: #6, 20, 26 + Sec 1.5: #4, 6, 11(a)

3. HW 3 (due on 9/23, Mon) Sec 1.6: #3, 6, 8, 13, 16 + Sec 2.1: #1, 3, 16 + Sec 2.2: #3, 5

4. HW 4 (due on 9/30, Mon) Sec 2.3: #5, 7,  17, 21, 26 + Sec 3.1: #1(a), 3(b), 6(a), 10(d), 20  

5. HW 5 (due on 10/7, Mon) Sec 3.2: #1(a), 3(d), 9 + Sec 3.3: #2 + Sec 4.1: #1(a), 2(a), 4, 9

6. HW 6 (due on 10/21, Mon) Sec 4.2: #1(b), #2(b); Sec 4.3: #1(a)(d)

7. HW 7 (due on 10/28, Mon)  Sec 4.4: #1; Sec 4.5: #1, 2, 6  

8. HW 8 (due on 11/4, Mon) Sec 4.7: #5, 9(b), 10(b) 

9. HW 9 (due on 11/22, FRI) Sec 5.1: #5(a), 6(b), 8, 11

10. HW 10 (*no need to submit) Sec 5.2: #5, 8, 9, 18, 19 

Tutoring Information: Visit at this department website.

Updates and Remarks - math221 - Fall 2019:

[12,6] Review session for Final Exam. Helpful note&partial solutions to Prac.Problm for Final Exam emailed.

[12,4] Sec 7.1, 1.7 diagonal, symmetric, orthogonal matrix / Review session for Final Exam. Graded Homework 9 and Quiz 9 are returned / Final Exam announced at D2L as well, Handout with details and  prac.probl. & guideline distributed and by E-mail and at D2L.

[12, 2] Sec 5.1-5.2 criterion for diagonalization, examples including the case of not-diagonalizable. Final Exam announced by email

[11, 22] Sec 5.1-5.2 more examples, criterion for diagonalization. Quiz 9 is taken.

[11, 20] Sec 5.1-5.2 concepts and definitions eigenvalue, eigenvectors, characteristic polynomial, examples. Graded Exam 3 returned with solution and grading rules.

[11,18] Sec 5.1-5.2 further motivating examples, some patterns in P^{-1}AP=D, examples.

[11, 15] Sec 5.1-5.2 introduced eigenvalue, eigenvectors, characteristic polynomial. 

[11,13] Exam 3 taken.

[11,8] Review session for Exam 2. Graded Homework 8 and Quiz 8 are returned./ Helpful note&partial solutions to Prac.Problm for Exam 3 emailed.

[11,6] Sec 5.1-5.2 more motivating examples for linear transformation and diagonalization. Exam 3 announced by email,D2L as well, Handout with details and prac.probl. & guideline distributed 

[11,4] Sec 5.1-5.2 motivating example for linear transformation and diagonalization. Quiz 8 is taken.

[11,1] Sec 4.7 examples for finding a basis consisting entirely of given vectors, rank+dimension of null space = # of columns. Graded Homework 7 and Quiz 7 are returned.

[10,30] Sec 4.7 technique to get dim/basis for row, column spaces using (reduced) row echelon form, examples, applications, dim of row space = dim of column space = rank. 

[10,28] Sec 4.7 defined row, column vectors and spaces, examples. HW 8 (due on 11/4, Mon) is assigned / Quiz 7 is taken.

[10,25] Sec 4.5 get basis and dimension of solution space using row echelon forms, #variables - #leading 1's. Graded Homework 6 is returned.

[10,23] Sec 4.3-4.5 more interpretation/examples for basis, definition, related questions for solution spaces, examples, suggested to use row reduced echelon form for finding dimension of solution spaces. 

[10,21] Sec 4.3-4.5 more examples for lin indep and Span(X), defined a basis and dimension, examples, meaning of two requirements, technique to check if it is a basis with dimension information - given dim V= n, a set of n vectors that they are linearly indep or n vectors that span V is a basis for V. HW 7 (due on 10/28, Mon) is assigned.

[10,18] Sec 4.3-4.5 more examples for lin indep, det(A) and lin indep, Span(X), examples, Span(X) is a subspace of V.

[10,16] Sec 4.3 motivating examples for lin independence, definition, techniques, examples. Graded Exam 2 returned with solution and grading rules, reviewed questions on Exam 2.

[10,14] Sec 4.2-4.3 Subspace, motive, examples, 'subspace criterion,' geometric meaning.

[10,11] Exam 2 taken.

[10,9] Review session for Exam 2. Graded Homework 5 and Quiz 5 are returned.

[10,7] Sec 4.1-4.5 examples for inner(dot) product, unit and opposite vector, more examples for zero-vector and negative vector. HW 6 (due on 10/21, Mon) is assigned / Quiz 5 is taken.

[10,4] Sec 4.1-4.5 full definition of general v.s. over R, examples, zero-vector, negative-vector, examples. Exam 2 announced by email,D2L as well, Handout with details and prac.probl. distributed / Graded Homework 4 and Quiz 4 are returned.

[10,2] Sec 3.1-3.3 more examples for inner product, |v||w|cos(theta) and its relation to the definition / Sec 4.1-4.5 motives for getting a general concept of vectors and vector spaces. Extra assignment (due on 10/9, Wed) is E-mailed.

[9,30] Sec 3.1-3.3 inner(dot) product, examples, dot product with non-zero vectors = 0 iff orthogonal(perpendicular), full general inner product to Euclidean vector space. HW 5 (due on 10/7, Mon) is assigned / Quiz 4 is taken.

[9,27] Sec 3.1-3.3 general conception of R^n, vector addition, scalar multiplication, examples, PQ=OQ-OP, two questions about other tools in vector spaces; abstract definition of vector spaces. Graded Homework 3 and Quiz 3 are returned.

[9,25] Sec 3.1 two motivating examples for vectors, introduced vectors <a,b> and their addition on xy-plane. Graded Homework 2 and Quiz 2 are returned.

[9,23] Sec 2.1-2.3 more examples, arguments for det(A), one can have AB=0 with non-zero matrices A, B, AB not equal BA in general. HW 4 (due on 9/30, Mon) is assigned / Quiz 3 is taken.

[9,20] Sec 2.1-2.3 connection det with 3 row elementary operations, examples, det(AB)=det(A)det(B), det(A^T)=det(A), examples.

[9,18] Sec 2.1-2.3 defined determinant for nxn, properties, examples.

[9,16] Sec 1.6 summarize inverse matrix related arguments, example / Sec 2.1-2.3 introduced determinant. HW 3 (due on 9/23, Mon) is assigned / Quiz 2 is taken.

[9,13] Sec 1.5-1.6 formula for inverse matrix of 3x3, and explained the pattern, examples, elementary way to get A^{-1} using 3 row elementary operations, example, application to solving a system of linear equations using A^{-1}, example.

[9,11] Graded Exam 1 returned with solution, reviewed questions on Exam 1.

[9,9] Sec 1.5-1.6 inverse matrices revisited, identity matrix, recalled definition of identity and inverse matrices from the concept in real numbers, examples, formula to get the inverse matrix for 2x2 cases. HW 2 (due on 9/16, Mon) is assigned.

[9,6] Exam 1 taken

[9,4] Sec 1.5 inverse matrices, examples.

[8,30] Sec 1.3-1.4 motivating matrix, matrix operations, definition of matrix, introduced +, -, multiplication, new terms, examples. Exam 1 announced by email,D2L as well, Handout with details distributed.

[8,28] Sec 1.3 more examples, clarification of row echelon form and reduced row echelon form, answered why there are three types of solutions and how to deal with parametric equations when answering the case of infinitely many solutions. Graded Homework 1 and Quiz 1 are returned.

[8,26] Sec 1.3 row echelon form, reduced row echelon form, Gauss-Jordan elimination, Gaussian elimination, examples, two unanswered questions regarding three types of solutions and parametrization for infinite many solutions. Quiz 1 is taken.

[8,23] Sec 1.1-1.2 three elementary row operations, augmented matrix, examples, remarks related to augmented matrix.

[8,21] Sec 1.1 general form of a system of linear equations, three types of solutions, consistent, inconsistent, examples, technique to solve a system of linear equations.

[8,19] Syllabus has been distributed in class, discussed syllabus, objectives - system of liner equations, matrices, vector spaces / Sec 1.1 Gave examples for linear equations, what is solving a system of linear equations. HW 1 (due on 8/26, Mon) is assigned.

[8,15] Uploaded syllabus on course website and D2L. HW 1 assigned.