Math221_F18

Introduction to Linear Algebra

- Fall 2018 -

Instructor: Kwangho Choiy

Course Website: https://sites.google.com/site/kchoiy/teaching/math221_f18

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 Aug. 14th.

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

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.*

Tutoring Information: COS Study Area Tutoring: Monday - Thursday 4-9 p.m

Updates and Remarks - math221 - Fall 2018:

[12/7, Fri] Review for Final

[12/5, Wed] Review for Final

[12/3, Mon] Section 5.2 - more examples for diagonalizable argument. HW9/Q9 are returned /  Final Exam (10:15-12:15 on 12/14, Fri) is announced in class, by email, D2L.

[11/30, Fri] Section 5.2 - criterion about whether or not to be diagonalizable, examples.

[11/28, Wed] Section 5.2 - examples for diagonalization, reason to be diagonalized using eigenvalues/vectors. HW8/Q8 are returned / HW 9 is collected / Quiz 9 is taken / Questions of HW 10 (no-need-to-submit) are given - **those are for Quiz 10 that will be taken on 12/5(Wed).

[11/26, Mon] Section 5.2 - motivation, obstacles of diagonalization, review of eigenvectors and eigenvalues, example for diagonalization. 

[11/16, Fri] Section 5.1 - introduce eigenvectors, eigenspace, examples.

[11/14, Wed] Section 5.1 - introduce eigenvalues, characteristic equation, examples. HW 8 is collected / Quiz 8 is taken. / HW 9 (due on 11/28, Wed) is assigned.

[11/12, Mon] Section 4.7&4.8 - introduced nullity and rank, nullity+rank=#of columns. how to use the null space (basis for the null space) to find solutions to system of linear equations. Graded HW7 is returned.  

[11/9, Fri] Section 4.7 - null space, examples, basis, dimension for the null space.

[11/7, Wed] Section 4.7 - more examples/ why the algorithm works out. HW 7 is collected / HW 8 (due on 11/14, Wed) is assigned

[11/5, Mon] Section 4.7 - more examples/remarks for finding a basis for row/column spaces.

[11/2, Fri] Section 4.7 - defined row, column vectors, spaces, examples, algorithm to find a basis for row, column spaces.

[10/31, Wed] Reviewed Exam 2 / outline for upcoming sections, introduced topics, motivatation. Graded Exam 2 is returned with solution /  HW 7 (due on 11/7, Wed) is assigned.

[10/29, Mon] Exam 2 is taken.

[10/26, Fri] Reviewed for Exam 2.

[10/24, Wed] Section 4.5 - solution spaces, examples to find a basis/dimension for solution spaces, helpful remarks. Graded HW6/Q6 are returned. 

[10/22, Mon] Section 4.4/Section 4.5 - more examples for basis, how to show a given set spans V. HW4/Q4 are returned. Exam 2 (10/29, MON) is announced in class, on website, D2L.  Graded HW5/Q5 are returned. 

[10/19, Fri] Section 4.4 - more about basis, examples to check whether a given subset is a basis / Section 4.5 - definition of dim, two remarks for dim, lin indep, span, example. HW 6 is collected / Quiz 6 is taken.

[10/17, Wed] Section 4.3 - more examples for linear independence, examples related to that det is not equal to 0 iff they are linear independent. / Section 4.4 - span, definition of basis, example.

[10/15, Mon] Section 4.2 - more examples subspace, geometric interpretation of subspaces in R^2, R^3 / Section 4.3 - motivating examples for linear independence, definition, example.

[10/12, Fri] Section 4.2 - introduced subspace, simple subspace criterion, examples. HW 5 is collected / Quiz 5 is taken / HW 6 (due on 10/19, Fri) is assigned.

[10/10, Wed] Section 4.1 - checked axioms with two distinct additions, scalar multiplications on R^2, additional motivation to study vector spaces. Graded HW4/Q4 are returned. 

[10/8, Mon] Section 4.1 - examples for vector spaces, giving two distinct additions, scalar multiplications to R^2.

[10/5, Fri] Section 3.1&3.3 - applications of inner products / Section 4.1 - introduced a general vector space.  HW 4 is collected / Quiz 4 is taken / HW 5 (due on 10/12, Fri) is assigned.

[10/3, Wed] Section 3.1-3.3 - properties of inner product, geometric meanings, applications, examples.

[10/1, Mon] Section 3.1-3.3 - more example for PQ=OQ-OP, defined norm/magnitude/length, inner product, examples.

[9/28, Fri] Section 3.1-3.3 - vectors, more examples, introduced R^n, Euclidean vector spaces, properties, linear combination, arrows as vector, parallelogram rule, PQ=OQ-OP. HW 4 (due on 10/5, Fri) is assigned.

[9/26, Wed] Section 3.1 - motivating example for vectors, introduced vectors, operations + -, scalar multiplication / reviewed Exam 1. Graded Exam 1 is returned with solution. 

[9/24, Mon] Exam 1 is taken.

[9/21, Fri] Reviewed for Exam 1. Graded HW3/Q3 are returned. 

[9/19, Wed] Section 2.1-2.3 - properties of determinant, examples.

[9/17, Mon] Section 2.1-2.3 - determinant and inverse matrices for general nxn matrices.  HW 3 is collected / Quiz 3 is taken / Exam 1 (9/24, MON) is announced in class, on website, D2L.

[9/14, Fri] Section 1.5&1.6 - more examples for inverse matrix algorithm, formula, elementary matrices, cases when the inverse DNE and examples. Graded HW2/Q2 are returned. 

[9/12, Wed] Section 1.5&1.6 - the inverse matrix using row elementary operations, defined elementary matrices and interpreted row elementary operations by multiplying LHS of the matrix by  elementary matrices.

[9/10, Mon] Section 1.3&1.4 - determinant, more examples, arguments for inverse matrices.  HW 2 is collected / Quiz 2 is taken / HW 3 (due on 9/17, Mon) is assigned.

[9/7, Fri] Section 1.3&1.4 - more arguments related to inverse matrix, inverse of 3x3 matrix, examples, when the inverse exists or not, transpose, scalar multiplication.

[9/5, Wed] Section 1.3&1.4 - matrix multiplication, two new phenomena (AB not euqal BA; AB=0 does not imply A=0 or B=0), examples, definition of inverse, identity matrix, form of the inverse matrix of 2x2 matrix. Graded HW1/Q1 are returned.

[8/31, Fri] Section 1.3&1.4 - three remarks from the motivating example -- commutativity, concept of inverse, existence of inverse related to matrix multiplication, basic terms for matrices. HW 1 is collected / Quiz 1 is taken / HW 2 (due on 9/10, Mon) is assigned

[8/29, Wed] Section 1.2 - more examples for reduced row epsilon matrix, Gaussian-Jordan elimination, parameterization, 3 elementary row operations / Section 1.3&1.4 - motivating example for why we need matrices and their operations.

[8/27, Mon] Section 1.2 - definition and examples of row epsilon, reduced row epsilon matrix, Gaussian elimination, Gaussian-Jordan elimination, parameterization for infinitely many solution cases.

[8/24, Fri] Section 1.2 - augmented matrix, three elementary row operations, examples, introduced reduced row epsilon matrix. HW 1 (due on 8/31, Fri) is assigned

[8/22, Wed] Sectoin 1.1 - consistence, inconsistence, three distinct types of solutions, connection to geometry, introduce three steps to get solutions, examples

[8/20, Mon] Syllabus distributed in class. Discussed main objectives of the course; Section 1.1 - introduced new terms with examples

[8/14, Tue] Supplementary Material: Visit the link to see mathematical proofs, notation, arguments, etc.