• Lecture: MWF 1000am-1050am
• Prerequisites: Mathematics 2J or 4.
• Mathematics 3A and 6G may not both be taken for credit.
• Textbook: Linear Algebra with Applications by S. Leon (7th Edition). We will go over Chapters 3-5.
• Midterm: May 1, Friday, in class.
• Final: June 8, Monday, 1030-1230.

 

Instructor

• Instructor: Shingyu Leung
• Email: syleung (at) math.uci.edu
• Office: Rowland Hall 510V
• Office Hours: MW 2-3, or by appointment.
• Homepage: http://www.math.uci.edu/~syleung/3a.09s/

 

Teaching Assistant

• Teaching Assistant: Robert Campbell
• Email: rcampbel (at) math.uci.edu
• Office Hour: W 11-12 RH 425
• Tutoring Hour: Tue 11-12 RH 594

• 04/15/09
  About the example I showed today in the class with {1, cos2x, cos^2 x},
  W(x)=0 for all x
  and so you CANNOT conclude that they are l.d. In this case, we have to go back to the definition of l.d. and check if we can find non-trivial c1,c2,c3 to solve the equation
  c1*1+c2*cos2x+c3*cos^2 x=0. (*)
  here, we use the angle formula
  cos2x=2cos^2 x-1
  and so, (*) becomes
  (c1-c2)+(2*c2+c3) cos^2 x =0 .
  We are now free to pick, for example, c2=1, -> c1=1 and c3=-2, which is a non-trivial solution to (*). now, we have l.d. for {1, cos2x, cos^2 x}.
  -------------
  Similarly, for HW2 Chapter3.3 Q8, we will need to use the angle formula
  cos x = 1- 2 sin^2(x/2)
  to show that those functions are l.d.
  -------------
  I am sorry that I wont be able to make it for class on friday. Prof. Song will substitude me this friday 4/17. He will start Chapter 3.5.

• 03/30/09
  1) I copied wrong from my note. The grading system should be
  20% HW + 15% Quiz + 25% MT + 40% Final.
  2) On tuesdays, the TA will discuss the HW.
  3) There is no quiz this week.
  4) HW1 will due next thursday (4/9) and Quiz1 on the same day.

Your grade will be determined according to 20% homework, 15% quizzes, 25% midterm and 40% final.

Homework will be assigned more or less weekly. They will be collected on Thursday in the discussion class. Only a portion of these homework problems will be graded. You will find the problems, with their corresponding deadlines, in the course homepage. No late homework will be collected. TA will discuss homework problems during discussion sections on Tuesday. The lowest score will be dropped.

• HW 1. Due Thursday 4/9.
  • Chapter 3.1: 3, 10, 11.
  • Chapter 3.2: 1(b,d), 3(d,g), 4(c), 6(b,d).
• HW 2. Due Thursday 4/16.
  • Chapter 3.2: 10(a,e), 11, 12.
  • Chapter 3.3: 2(b,d), 5, 6(b), 8, 14.
• HW 3. Due Thursday 4/23.
  • Chapter 3.4: 2(b,d), 3, 7, 8, 14(c,d), 15
  • Chapter 3.5: 5(b)
• HW 4. Wont be collected, but you should try them.
  • Chapter 3.5: 6, 10
  • Chapter 3.6: 1(b), 4(c), 8, 9, 11, 13, 21
• HW 5. Due Thursday 5/7.
  • Chapter 4.1: 3, 7(d), 8(c), 10, 16, 24
• HW 6. Due Thursday 5/14.
  • Chapter 4.2: 3(c), 6, 13, 14(b), 15, 18(b)
  • Chapter 4.3: 1(a), 2
• HW 7. Due Thursday 5/21.
  • Chapter 4.3: 5, 6, 7, 12
  • Chapter 5.1: 15, 16
  • Chapter 5.2: 1(c)
• HW 8. Due Thursday 5/28.
  • Chapter 5.2: 3, 4, 9, 17
  • Chapter 5.4: 3, 9, 11(c), 26 (a,c)
• HW 9. Wont be collected, but you should try them.
  • Chpater 5.5: 4, 6, 14, 28(a-b)
  • Chapter 5.6: 1(a), 3, 4, 5

• HW1
• HW2
• HW3
• HW4
• HW5
• HW6-9

Quiz will be assigned weekly in the discussion class on Thursday. The lowest score will be dropped.

There will be one midterm exam and one final exam. The final exam will be comprehensive. No makeup exam will be given. All the exams in this course are "closed book" -- no books, notes, calculators, PDAs, cell phones, etc.

• Midterm V1
• Midterm V2
• Midterm Solution (Robert Campbell)
• Final V1
• Final V2
• Final V1 Solution

• Vector Spaces (Sections 3.1-3.6): 10 lectures
  • Definition and Examples
  • Subspaces
  • Linear independence
  • Basis and Dimension
  • Change of basis
  • Row Space and Column Spaces
• Linear Transformations (Sections 4.1-4.3): 6 lectures
  • Definition and Examples
  • Matrix representation of linear transformations
  • Similarity
• Orthogonality (Sections 5.1-5.5): 11 lectures
  • Scalar product in R^n
  • Orthogonal subspaces
  • Least square problems
  • Inner product spaces
  • Orthonormal sets
  • Orthogonal Polynomial

• 03/30 Mon Lecture 1: Overview. Notations.
  Reading:
• 04/01 Wed Lecture 2: Vector Spaces. Definitions.
  Reading: Chapter 3.1
• 04/03 Fri Lecture 3: Definition of Subspace and Nullspace.
  Reading: Chapter 3.2
  
  
• 04/06 Mon Lecture 4: Linear combination, span, spanning set.
  Reading: Chapter 3.2
• 04/08 Wed Lecture 5: Linear independence. Definitions of "linearly independent", "linear dependent".
  Reading: Chapter 3.3
• 04/10 Fri Lecture 6: Linear independence for the vector spaces R^n, P_n, C.
  Reading: Chapter 3.3
  
  
• 04/13 Mon Lecture 7: Definition of basis, standard basis, dimension.
  Reading: Chapter 3.4
• 04/15 Wed Lecture 8: Examples on basis and dimension. Definition of Coordinates.
  Reading: Chapter 3.4, 3.5
• 04/17 Fri Lecture 9: Change of basis in Rn.
  Reading: Chapter 3.5
  
  
• 04/20 Mon Lecture 10: Change of basis in Rn and general vector space V. Row space and Column space.
  Reading: Chapter 3.5, 3.6
• 04/22 Wed Lecture 11: Rank. Rank-Nullity Theorem.
  Reading: Chapter 3.6
• 04/24 Fri Lecture 12: Example on computing Rank, column space. Definition of Linear Transformation.
  Reading: Chapter 3.6 and Chapter 4.1
  
  
• 04/27 Mon Lecture 13: Linear Transfomation. Definition of kernal, image, range.
  Reading: Chapter 4.1
• 04/29 Wed Lecture 14: Kernal and Range. Matrix representation of linear transformations between Rn and Rm.
  Reading: Chapter 4.1, 4.2
• 05/01 Fri Lecture 15: Midterm
  Reading:
  
  
• 05/04 Mon Lecture 16: Matrix representation of linear transformations between vector spaces.
  Reading: Chapter 4.2
• 05/06 Wed Lecture 17: Similarity
  Reading: Chpater 4.3
• 05/08 Fri Lecture 18: Diagonalization. Scalar product in Rn.
  Reading: Chpater 4.3, 5.1
  
  
• 05/11 Mon Lecture 19: Orthogonal subspaces.
  Reading: Chapter 5.2
• 05/13 Wed Lecture 20: Orthogonal subspaces.
  Reading: Chpater 5.2
• 05/15 Fri Lecture 21: Inner product space.
  Reading: Chapter 5.4
  
  
• 05/18 Mon Lecture 22: Inner product space.
  Reading: Chapter 5.4
• 05/20 Wed Lecture 23: Orthonormal sets.
  Reading: Chapter 5.5
• 05/22 Fri Lecture 24: Orthonormal sets.
  Reading: Chapter 5.5
  
  
• 05/25 Mon Lecture 25: Holiday
  Reading:
• 05/27 Wed Lecture 26: Orthonormal sets. The Gram-Schmidt process.
  Reading: Chapter 5.5, 5.6
• 05/29 Fri Lecture 27: The Gram-Schmidt process.
  Reading: Chapter 5.6
  
  
• 06/01 Mon Lecture 28: The Gram-Schmidt process. Least square solution.
  Reading: Chapter 5.6
• 06/03 Wed Lecture 29: Review.
  Reading:
• 06/05 Fri Lecture 30: Review.
  Reading: