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.

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: Halyun Jeong

Office hours: 5-6 pm on Tue, 4-5pm on Wed in LSK 300.

Email: hajeong@math.ubc.ca

All exams are closed books and no calculators are allowed.

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 #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.

The WeBWorK link: Webwork

If this link doesn't work for some reason then you should

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.