Mathematics 1104A

Linear Algebra for Engineering or Science

 

Course Outline

TA's names.

F1: Abdulaziz Dahir. Office hours: Monday 10-11 AM, HP3361.

F2: Steven Wu. Office hours: 4:00 - 5:00 pm on Wednesdays in MTC 1160

F3: Aly Gemae, Office hours: 1pm to 2pm on Mondays in MTC 1160.

F4: David Bui, Office hours: Monday: 4:30pm - 5:30pm, in MTC 1160.

Extra help can be found from Math Tutorial Centre, 10am -4pm, Monday to Thursday, at HP1160.

 

Topics covered in the class

  • Jan. 7: Introduction & system of linear equations.
  • Jan. 9: Solutions of system of linear equations, elementary row operations, row echlon form.
  • Jan. 14: Solve a system of linear equations.
  • Jan. 16: Matrices.
  • Jan. 21: Matrix operations and properties.
  • Test #1 covers up to here.
  • Jan. 23: Invertible matrices and elementary matrices.
  • Jan. 28: elementary matrices and LU factorization
  • Jan. 30: Invertible matrix theorem, Determinants
  • Feb. 4: properties of determinants.
  • Feb. 6: Applications of Determinants (adjoints, cramer's rule, area and volume)
  • Test #2 covers up to here.
  • Feb. 11: R^n and vector spaces.
  • Feb. 13: subspace, spanning set.
  • Feb 18-22: reading week.
  • Feb 25: review of vector spaces, subspaces and spanning set.
  • Feb 27: spanning set, linearly independence/dependence, basis.
  • Mar. 4: basis, dimension, row and column space.
  • Mar. 6: basis of row(column, null) space, rank theorem.
  • Mar. 11: more about row(column, null) spaces, data compression and change of basis.
  • Mar. 13: More change of basis, Search Web using eigenvectors. Eigenvalues/Eigenvectors.
  • Test # 3 covers chapter 4 (Sections 4.1-4.7).
  • Mar. 18: Eigenvectors and Diagonalization.
  • Mar. 20: Diagonalization, complex numbers.
  • Mar. 25: Polar forms, De Moirve's Theorem, complex eigenvalues.
  • Mar. 27: Complex eigenvectors, Diagaonlization, inner products.
  • Apr. 1: inner product, orthogonality.
  • Apr. 3: orthogonal basis, orthogonal projection, linear transformation.
  • Apr. 8: linear transformation and review.

    • Tutorials

  • Tutorial #1
  • Tutorial #2: Section 1.2: 49; Section 2.1: 11, 15, 19, 39 (solutions are in the textbook).
  • Tutorial #3: Section 2.2: 47; Section 2.3: 47, 63; Section 2.4: 1,3, 5, 7, 35, 45.
  • Tutorial #4: Section 3.1: 31, 39; Section 3.2: 35, 37; Section 3.3: 41, 55; Section 3.4: 3, 25, 37, 41.
  • Tutorial #5: Section 4.2: 27; Section 4.3: 29, 39, 43; Section 4.4: 1 (a), 21, 29, 41, 45, 59, 69; Section 4.5: 15, 35.
  • Tutorial #6: Section 4.5: 71. Section 4.6: 9, 23, 33, 47, 67
  • Tutorial #6: Section 4.7: 35. Section 7.1: 17, 23 Section 7.2: 7, 11, 13, 17, 37.
  • Tutorial #7: Section 4.7: 35. Section 7.1: 17, 23 Section 7.2: 7, 11, 13, 17, 37.
  • Tutorial #8: 1) Section 8.2: 15, 19, 21, 31. 2) Section 8.3: 27, 31, 35, 37, 45 3) If possible, diagonalize the 2x2 matrix as attached .

    PRACTICE PROBLEMS

  • 1.1: 1-51
  • 1.2: 11-37, 41-43
  • 2.1: 1-29, 31-40, 43-48, 50-52
  • 2.2: 1-13, 15-19, 23-28, 31-34, 37-42
  • 2.3: 1-5, 7-24, 31-35, 41-44, 46-48
  • 2.4: 1-7, 13-16, 18-21, 23-33
  • 2.5: 24-26
  • 3.1: 1-16, 19-27, 33, 34, 39-42
  • 3.2: 21-23, 25-33, 37, 38
  • 3.3: 1-5, 7-11, 13-15, 17-23, 25-28, 37-43
  • 3.4: 1-7, 17-29, 37-39, 41-43, 45-47, 49-51, 53-55, 57-59, 61, 62
  • 4.1: 7-25,33-35, 45-48
  • 4.2: 1-13
  • 4.3: 1-4, 7-10
  • 4.4: 1-3, 9-13, 49-53
  • 4.5: 7-12, 15-19, 33-38
  • 4.6: 1,3, 5-9, 11,13, 19-23, 25-32, 37-39, 47
  • 4.7: 1-4
  • 5.1: 1-7, 9-12, 14-16, 19-21, 23-27, 37-43, 53-55
  • 5.2: 17-25
  • 5.3: 1-13, 15-17
  • 6.1: 1-7, 9-14, 45
  • 6.2: 1-5, 11-15, 19-23
  • 6.3: 1-5
  • 7.1: 1-7, 11-13, 17-25
  • 7.2: 1-5, 7-13, 15,17, 33-35
  • 7.3: 1-4
  • 8.1: 7-9, 11-15, 17-21, 25, 27-33
  • 8.2: 1-11, 15-19
  • 8.3: 1-4, 5-13, 17-23, 35-41