# MATH 221: Matrix Algebra (2018 Term 2, Section 201)

## Announcement

The first lecture will be on Wednesday, January 2.

The first homework will be postd this week (probably on Jan 9).

Correction: The definition of (row) echelon form in the lecture note 3.
The leading entry of a row is the the left of the leading entry of the next row . Or the leading entry of a row is to the right of the leading entry of the row above it .

The first WebWork is now assigned (Due on Jan 16, 11:59 pm). If the link in the WebWork section is not working, please refresh your web broswer.

The WebWork #2 is posted (Due on Jan 23, 11:59 pm).

The WebWork #3 is posted (Due on Jan 30, 11:59 pm).

Midterm 1: Wednesday, February 6. In class (3 pm - 3:50 pm), closed book.
The midterm 1 is based on the follwoing material in the text book:
Chapter 1: All sections except the Homogeneous system in Economics part in section 1.6.

Here are the practice midterm problems:
Practice problem set 1   Solution
Practice problem set 2
Practice problem set 3

Office hours for midterm 1: Feb 4(Mon) 5-6pm, Feb 5(Tue) 4-5pm both in LSK 300.

The WebWork #4 is posted (Due on Feb 13, 11:59 pm).

The WebWork #5 is posted (Due on Mar 1, 11:59 pm).

Notation in WebWork #5:
Ker(A) = The null space of A = Nul A and Im(A) = The column space of A = Col A.

The WebWork #6 is posted (Due on Mar 8, 11:59 pm).

The WebWork #7 is posted (Due on Mar 15, 11:59 pm).

Midterm 2: Wednesday, March 20th. In class (3 pm - 3:50 pm), closed book. Here are the practice midterm problems:
Practice problem set 1   Solution
Practice problem set 2   Solution

Office hours for midterm 2: Mar 18(Mon) 5-6pm, Mar 19(Tue) 5-6pm both in LSK 300.

The WebWork #8 is posted (Due on Mar 29, 11:59 pm).

The WebWork #9 is posted (Due on Apr 5, 11:59 pm).

Final Exam: Thursday, April 25th. at 3:30 pm. Closed book. Here are the practice final exam problems:
Practice problem set 1
Practice problem set 2
Practice problem set 3

Office hours for the final exam: April 23 (Tuesday) 4-5:30 pm, April 24 (Wednesday) 4-6pm both in LSK 300.

## Course Information

Lectures: Mon, Wed, Fri 3pm-4pm at room 201, Leonard S. Klinck(LSK).
Course webpage: http://www.math.ubc.ca/~hajeong/MATH221_2018W2.html

Text book: Linear Algebra and its Applications by David C. Lay

## Instructor Information

Instructor: Halyun Jeong
Office hours: 5-6 pm on Tue, 4-5pm on Wed in LSK 300.
Email: hajeong@math.ubc.ca

## Course Outline

Outline

See the course outline (Syllabus) above.

## Exam Information

There will be two midterms and one final exam for this course.
Midterm 1: Wednesday, February 6. In class (3 pm - 3:50 pm), closed book.

All exams are closed books and no calculators are allowed.

## Lecture notes

Lecture 1 (02/01/2019) : I.1 Linear equations, A system of linear equations.

Lecture 2 (04/01/2019) : I.1 Solving a linear system.

Lecture 3 (07/01/2019) : I.1-I.2 Solving a linear system and Echelon form.
Correction: The definition of (row) echelon form .
The leading entry of a row is the the left of the leading entry of the next row . Or the leading entry of a row is to the right of the leading entry of the row above it .

Lecture 4 (09/01/2019) : I.2 Reduced echelon form and Solutions of Linear systems, I.3 Vectors and Linear combinations of vectors.

Lecture 5 (11/01/2019) : I.2 Pivots, I.3 Linear combinations of vectors, Span of vectors.

Lecture 6 (14/01/2019) : I.3 Span of vectors and I.4 Matrix equations.

Lecture 7 (16/01/2019) : I.4 Matrix equations, I.5. Homogeneous equations.

Lecture 8 (18/01/2019) : I.5. Homogeneous equations, the solution structure of nonhomogeneous equations.

Lecture 9 (21/01/2019) : I.6. Balancing chemical equations, Network flow.

Lecture 10 (23/01/2019) : I.6. Network flow, I.7 Linear independence.

Lecture 11 (25/01/2019) : I.7 Linear independence, I.8 Introduction to linear transformations.

Lecture 12 (28/01/2019) : I.8 Introduction to linear transformations, I.9 The matrix of a linear transformation.

Lecture 13 (30/01/2019) : I.8 Introduction to linear transformations, I.9 The matrix of a linear transformation.

Lecture 14 (1/2/2019) : I.8 Introduction to linear transformations, I.9 The matrix of a linear transformation. (This note is for the lecture 14 not 13)

Lecture 15 (4/2/2019) : II.1 Matrix operations.

Lecture 16 (8/2/2019) : II.1 Matrix operations.

Lecture 17 (11/2/2019) : II.2 The inverse of a matrix.

Lecture 18 (13/2/2019) : II.2 The inverse of a matrix, II.3 Characterization of invertible matrices.

Lecture 19 (15/2/2019) : II.3 Characterization of invertible matrices.

Lecture 20 (25/2/2019) : II.3 Characterization of invertible matrices and II.5 Subspace of R^n.

Lecture 21 (27/2/2019) : II.5 Subspace of R^n, II.6 Dimension and Rank.

Lecture 22 (1/3/2019) : II.6 Dimension and Rank.

Lecture 23 (4/3/2019) : III.1 Introduction to Determinants.

Lecture 24 (6/3/2019) : III.1 Introduction to Determinants, III.2. Properties of Determinants.

Lecture 25 (8/3/2019) : III.2. Properties of Determinants, IV.1 Eigenvalues and Eigenvectors.

Lecture 26 (11/3/2019) : IV.1 Eigenvalues and Eigenvectors.

Lecture 27 (13/3/2019) : IV.1 Eigenvalues and Eigenvectors, IV.2 The characteristic equation

Lecture 28 (15/3/2019) : IV.2 The characteristic equation

Lecture 29 (18/3/2019) : IV.3 Digonalization

Lecture 30 (22/3/2019) : IV.3 Digonalization

Lecture 31 (25/3/2019) : IV.3 Digonalization, IV.6. Discrete dynamical system

Lecture 32 (27/3/2019) : IV.6. Discrete dynamical system, V.1. Inner product, Length, Orthogonality.

Lecture 33 (29/3/2019) : V.1. Inner product, Length, Orthogonality, V.2. Orthogonal sets.

Lecture 34 (1/4/2019) : V.2. Orthogonal sets, V.3. Orthogonal projections.

Lecture 35 (3/4/2019) : V.3. Orthogonal projections, V.5. The least square problems.

## Webwork

WebWorK #1 is due Wednesday January 16 at 11:59pm.
WebWorK #2 is due Wednesday January 23 at 11:59pm.
WebWorK #3 is due Wednesday January 30 at 11:59pm.
WebWorK #4 is due Wednesday Feburary 13 at 11:59pm.
WebWorK #5 is due Wednesday March 1 at 11:59pm.
WebWorK #6 is due Wednesday March 8 at 11:59pm.
WebWorK #7 is due Wednesday March 15 at 11:59pm.
WebWorK #8 is due Wednesday March 29 at 11:59pm.
WebWorK #9 is due Wednesday April 5 at 11:59pm.

Notation in WebWork #5:
Ker(A) = The null space of A = Nul A and Im(A) = The column space of A = Col A.

If this link doesn't work for some reason then you should try accessing the webworks through canvas (logging into canvas and clicking the MATH221 ALL tab, then looking at the assignments) .

## Suggested problems (not to be handed in)

Section 1.1: #1,2,4,5,6,7-16,19-22,29-32.
Section 1.2: #1,2,7-14,15-20.
Section 1.3: #1,2,5,6,9-16,19-22,25-26.
Section 1.4: #1-4,5-10,11-15, 18-26.
Section 1.5: #1-4,7-10,13,14,17,18,19,20,23,24.
Section 1.6: #6-15.
Section 1.7: #1-4,5-8,11-14,15-20,21-22,33-38.
Section 1.8: #1-6,7-8,9-12,17,19,20.
Section 1.9: #1-10,15-22,22-28.
Section 2.1: #1-10,12,15-20,26.
Section 2.2: #1-8,9-24,29-32.
Section 2.3: #1-8,11-24,28-34.
Section 2.5: #1-8,15-20,21-26.
Section 2.6: #3-6,9-12,13-14,17-18,19-24.
Section 3.1: #5-7,19-24,25-30,32,37-38.
Section 3.2: #1-4,5-10,15-20,21-23,24-26,27,28.
Section 4.1: #1-18,21-24.
Section 4.2: #1-8,9-14,15-17,21-22.
Section 4.3: #1-20,21.
Section 5.1: #1-12,15-18,19-20.
Section 5.2: #1-6,7-16,17-22.
Section 5.3: #1-6,7-12,15-16,21.
Section 5.5: #1-4,9-13.