Schedule, Announcements, and Homework Assignments

Cumulative Final Exam: Tuesday, December 12th, 7:30pm to 10:30pm

Please remember to complete the online course evaluation before Sunday, December 10th.

Here Are Some Extra Practice Problems   (Solutions)
Practice problems for Section 6.2, 6.3 and 6.5     (Solutions)

Extra Office Hours:

Qi Gong: Monday, December 11th, 2:00pm - 4:00pm, BE 361A 

 Tuesday, December 12th, 10:30am - 12:00pm, BE 361A

Kenneth Galuya: Sunday, December 10th, 2:00pm - 4:00 pm, BE 312 C/D

Sky Trigueiro: Monday, December 11th, 7:00pm - 9:00pm, BE 312 C/D

Quiz #4 (In Lab Sections On 12/04 And 12/06): this quiz covers topics on eigenvalues and eigenvectors

Lecture #17 (11/30), #18 (12/05) and #19 (12/07): Read Section 6.1, 6.2, 6.3, 6.5 and 7.1.

Core Topics In Section 6.1, 6.2, 6.3 And 6.5
  1. Definitions of norm, distance, inner product and orthogonality 
  2. Theorem 2 (The Pythagorean Theorem) 
  3. Definition of orthogonal complement and Theorem 3 on the relation between Col A and Nul A 
  4. Definition of orthogonal set and orthogonal basis 
  5. Theorem 5 on expansion w.r.t. orthogonal basis
  6. Orthogonal Decomposition Theorem and The Best Approximation Theorem 
  7. Least square solution and Theorem 14 
  8. Definition of symmetric matrix
  9. Properties of symmetric matrix (Theorem 1 & 3)
  10. Diagonalization of symmetric matrix (Theorem 2)

     

Extra Reading Material for Section 6.1, 6.2, 6.3 and 6.5

Homework #8 (Due on Tuesday, 12/05/2017, at the beginning of the class)

Homework #8 — Solutions

Practice Problems in the Textbook (4th Edition)

Section 6.1: Exercises 1, 3, 13, 18, 19, 20, 23, 29, 30

Section 6.2: Exercises 1, 3, 9, 11, 15, 23, 24, 26

Section 6.3: Exercises 1, 4, 6, 9, 13, 15, 21, 22

Section 6.5: Exercises 3, 9, 11, 17, 18, 19

Lecture #15 (11/21) and #16 (11/28): Read Section 5.1, 5.2, 5.3 and 5.5.

Core Topics In Section 5.1, 5.2, 5.3 And 5.5
  1. Definitions of eigenvalue and eigenvector 
  2. How to compute eigenvalue and corresponding eigenvector 
  3. Definitions of characteristic equation and eigenspace 
  4. Properties of eigenvalue and eigenvector including Theorem 1 and Theorem 2 
  5. Definition of algebraic multiplicity and geometric multiplicity
  6. Definition of similarity transformation and Theorem 4
  7. Theorem 5, 6 and 7 on diagonalization

Extra Reading Material for Section 5.1, 5.2 and 5.3

Homework #7 (Due on Tuesday, 11/28/2017, at the beginning of the class)

Homework #7 — Solutions

Practice Problems in the Textbook (4th Edition)

Section 5.1: Exercises 6, 7, 13, 14, 21, 22, 26

Section 5.2: Exercises 7, 8, 15, 16, 17, 21, 22

Section 5.3: Exercises 2, 4, 15, 16, 18, 21-28

Section 5.5: Exercises 6, 22, 23 and 24

Quiz #3 (In Lab Sections On 11/20 And 11/22): this quiz covers topics on subspace and determinant

Lecture #13 (11/14) and #14 (11/16): Read Section 3.1, 3.2 and 5.1.

Core Topics In Section 3.1, Section 3.2, and Section 5.1
  1. Definition of determinant 
  2. Theorem 1 (cofactor expansions) 
  3. Theorem 2 on the determinant of triangular matrices 
  4. Properties of determinant (Theorem 3, 4, 5 and 6)
  5. Definitions of eigenvalue and eigenvector 

Homework #6 (Due on Tuesday, 11/21/2017, at the beginning of the class)

Homework #6 — Solutions

Practice Problems in the Textbook (4th Edition)

Section 3.1: Exercises 9-12, 15, 16, 23, 24, 39, 40

Section 3.2: Exercises 8, 9, 15-20, 25-28, 30, 35

Starting from this week, homework is due on Tuesdays at the beginning of the class.

Lecture #11 (11/07) and #12 (11/09): Read Section 2.8, 2.9 and related topics in Chapter 4 (Section 4.1 to 4.7).

Core Topics In Section 2.8, 2.9 and Section 4.1 to 4.7
  1. Definitions of subspace, basis, dimension, coordinate, column cpace, null space, and rank 
  2. How to find a basis for Col(A) and Nul(A). 
  3. How to compute dim(Col(A)), rank(A) and dim(Nul(A)). 
  4. Theorem 12, 13, 14, 15 and The Invertible Matrix Theorem 
  5. The Spanning Set Theorem (Theorem 5 in Sec. 4.3) 
  6. The Unique Representation Theorem (Theorem 7 in Sec. 4.4)

Extra Reading Material for Section 2.8-2.9 and Chapter 4

Homework #5 (Due on Tuesday, 11/14/2017, at the beginning of the class)

Homework #5 — Solutions

Practice Problems in the Textbook (4th Edition)

Section 2.8: Exercises 1-4, 7, 9, 13, 21, 22, 27-36

Section 2.9: Exercises 1, 5, 7, 13, 19-28

Midterm Exam: Thursday, 11/02/2017.

midterm exam covers: complex numbers, Section 1.1, 1.2, 1.3, 1.4, 1.5, 1.7, 2.1, 2.2 and 2.3. You can use Homework #1 to #4, practice problems in the textbook, and the following practice problems to prapare for the midterm exam.

Practice Problems for midterm exam  ----- (Click Here for Solutions)

Lecture #9 (10/26) and #10 (10/31): Read Section 2.2 and 2.3 of the Textbook

Core Topics In Section 2.2 & 2.3.
  1. Definition of invertible matrix. 
  2. Theorem 5, 6, and 7. 
  3. How to compute the inverse of a matrix. 
  4. Theorm 8 (The Invertible Matrix Theorem)

Extra Reading Material for Section 2.2 & 2.3

Homework: due to midterm exam, there is no homework this week. 

Practice Problems in the Textbook (4th Edition)

Section 2.2: Problem 3, 6, 7, 9, 10, 14, 21-24, 35, 37

Section 2.3: Problem 1-8, 11, 12, 15-18, 21, 23 

Quiz #2 (In Lab Sections On 10/23 And 10/25):this quiz covers topics in section 1.1, 1.2, 1.3, & 1.4.

Lecture #7 (10/19) and #8 (10/24): Read Section 1.7 and 2.1 of the Textbook

Core Topics In Section 1.7 & 2.1
  1. Definitions of linearly dependent/independent set of vectors. 
  2. Relation of linear dependence of matrix columns and the solution of homogeneous equations. 
  3. How to verify a given set of vectors is linearly dependent or not; and how to find a linear dependence relation. 
  4. Theorem 7, 8 and 9. 
  5. Definitions of diagonal matrices, zero matrices and identity matrices. 
  6. Scalar multiplication and matrix addition. 
  7. How to compute matrix multiplication (by definition and row-column rule). 
  8. Definitions of powers and transpose of a matrix. 
  9. Theorem 1, 2 and 3 on the properties of matrix operations.

Homework #4 (Due on Thursday, 10/26/2017, at the beginning of the class.)

Homework #4 — Solutions

Lecture notes on matrix applications and matrix operations

Extra Reading Material for Section 1.7 & 2.1

Practice Problems in the Textbook (4th Edition)

Section 1.5: Problem 4, 6, 13, 23, 24, 32, 35

Section 1.7: Problem 6, 8, 14, 15, 16, 21, 22, 34-38, 40 

Section 2.1: Problem 2, 4, 6, 10, 12, 13, 15, 16,17, 27 

Lecture #5 (10/12) and #6 (10/17): Read Section 1.3, 1.4 and 1.5 of the Textbook

Core Topics In Section 1.3 & 1.4
  1. Definitions of vector, Rn, linear combination, vector equation and span. 
  2. Understand the equivalence between vector equation and system of linear equations. 
  3. Understand geometric description of span in R2 and R3. 
  4. How to define the product of a matrix and a vector. 
  5. Definition of matrix equation. 
  6. Theorem 3 and Theorem 4 in Section 1.4. 
  7. How to use row-vector rule to compute Ax. 
  8. Properties of matrix-vector product (Theorem 5).

Core Topics In Section 1.5 

  1. Definition of homogeneous equation. 
  2. Know how to write the solution set of homogeneous equation in parametric vector form. 
  3. Theorem 6 on the structure of solution set for Ax=b.

Homework #3 (Due on Thursday, 10/19/2017, at the beginning of the class.)

Homework #3 — Solutions

Extra Reading Material for Section 1.3 & 1.4

Extra Reading Material for Section 1.5

Practice Problems in the Textbook (4th Edition)

Section 1.3: Problem 3, 5, 10, 12, 14, 18, 23, 24, 25

Section 1.4: Problem 2, 8, 10, 13, 23, 24, 29, 30, 31 

Quiz #1 on complex Numbers (in lab sections on 10/09 and 10/11)

Lecture #3 (10/10) and #4 (10/12): Read Section 1.1 and 1.2 of the Textbook

Core Topics In Section 1.1 & 1.2
  1. Definitions of Linear Equation, System of Linear Equations, Solution Set, Equivalent Systems, Consistent/inconsistent Equations. 
  2. Definitions of Coefficient Matrix and Augmented Matrix. Know how to write down Coefficient (Augmented) Matrix for any linear systems. Know how to find corresponding linear systems based on augmented matrix. 
  3. Definitions of the three Elementary Row Operations (Replacement, Interchange, Scaling) 
  4. Definitions of Echelon Form and Reduced Echelon Form. 
  5. Definitions of Pivot Positions and Pivot Columns. 
  6. Theorem 1 on Uniqueness of the reduced echelon form. 
  7. The Row Reduction Algorithm (Step 1 - 5 summarized in Section 1.2). Know how to apply this algorithm to row reduce any matrix into its reduced echelon form. 
  8. Definitions of Basic Variables and Free Variables. 
  9. How to use elementary row operations to solve a linear system. 
  10. Theorem 2 (Existence and Uniqueness Theorem in Section 1.2)

Homework #2 (Due on Thursday, 10/12/2017, at the beginning of the class.)

Homework #2 — Solutions

Extra Reading Material for Section 1.1 & 1.2 

Lecture #1 (09/28) and #2 (10/03): Read Katznelson's notes on complex algebra (A Primer on Complex Numbers - PDF)

Core Topics in Complex Numbers
  1. Definition of imaginary number, complex number, real and imaginary parts of complex numbers, complex conjugate. 
  2. Complex arithmetic including addition, subtraction, multiplication and division. Proposition 2.1, 2.2 and 2.3 in lecture notes.
  3. Definition of complex plane, modulus (absolute value) and argument (phase). 
  4. Representation of complex numbers in rectangular and polar coordinates. Transformation between rectangular coordinates and polar coordinates. Proposition 3.1, 3.2, 3.3, 3.4, 3.5 and 3.6 in lecture notes.
  5. Euler's formula and exponential notation of complex numbers (Proposition 3.7 and 3.8). How to use Euler's formula to compute nth roots (Proposition 4.8).
  6. Properties of polynomial equations with real coefficients, including number of roots and Proposition 4.5. 

Homework #1 (Due on Thursday, 10/05/2017, at the beginning of the class.)

Homework #1 — Solutions

Practice Problems in the Lecture Notes 

Exercises 1.1, 1.2 (page 3), Exercises 2.2, 2.6, 2.7 (page 6), Exercises 3.1, 3.6, 3.7 (page 15), Exercises 4.2, 4.7 (page 21-22)