Linear Algebra Fall 2016

Course Syllabus: Click here.

Weekly Schedule: Announcements about homework, quizzes, exams, special lectures, etc. will be posted here.

  • Week of August 1st.

Lecture 1 (01/08/16): Fields, and some related notions like groups, rings, characteristic of a field.

Lecture 2 (02/08/16): Systems of linear equations; equivalent systems; geometric meaning.

Tutorial 1 (05/08/16): Get to know your tutors; discuss homework 1; Quiz 1.

Homework 1: Click here.

  • Week of August 8th.

Lecture 3 (08/08/16): Elementary row operations; row-equivalence of matrices.

Lecture 4 (09/08/16): Row-reduced echelon matrices; a homogenous system in fewer equations than variables has nontrivial solutions.

Homework 2: Click here.

Lecture 5 (12/08/16): From 9:00 to 10:00, in LHC 103. Matrix multiplication and elementary matrices.

Lecture 6 (12/08/16): 10:10 to 11:10, in LHC 103, Invertible matrices.

Homework 3: Click here.

Tutorial 2 (12/08/16): Discuss Homework 2; Quiz 2. (All sections will meet from 4:20 to 5:20 p.m. in their respective rooms in LHC.)

  • Week of August 15th.

August 15th: Independence day.

August 16th: No lecture.

Tutorial 3 (19/08/16): Discuss Homework 3; Quiz 3.

  • Week of August 22nd.

Lecture 7 (22/08/16): What is a vector space? Examples.

Lecture 8 (23/08/16): Linear combination, Vector subspace, Span of a set of vectors, A sum of subspaces.

Homework 4: Click here.

Tutorial 4 (26/08/16): Discuss Homework 4; Quiz 4.

  • Week of August 29th.

Lecture 9 (29/08/16): Linear independence of vectors, basis, "any two bases of a finite-dim vector space have the same number of vectors"

Lecture 10 (30/08/16): Bases and dimension, continued.

Homework 5: Click here.

Tutorial 5 (02/09/16): Discuss Homework 5; Quiz 5.

  • Week of September 5th.

September 5th is a holiday.

Lecture 11 (06/09/16): Coordinates of a vector w.r.t an ordered basis; change of basis matrix.

Homework 6: Click here.

Tutorial 6 (09/09/16): Discuss Homework 6; Quiz 6.

  • Week of September 12th.

September 12th is a holiday.

Lecture 12 (13/09/16): Computations with a matrix: row space, null space, invertibility; determining the dimension of a span of vectors, etc.

Homework 7: Click here.

Tutorial 7 (16/09/16): Discuss Homework 7; Quiz 7.

  • Week of September 19th = Week of mid-semester exams.

Mid-term exam for Linear Algebra (MTH 201) is scheduled from 3:00 to 5:00 p.m. on Tuesday, September 20th.

Syllabus: Everything covered so far; the first seven homework sets; this corresponds to the first two chapters of Hoffman and Kunze's book.

Past exams that you may use for practice: Exam-1, Exam-2.

  • Week of September 26th.

Lecture 13 (26/09/16): Discuss exam; get started on Linear Transformations.

Lecture 14 (27/09/16): "Rank+Nullity" theorem. Row-Rank(A) = Column-Rank(A) for any matrix A.

Homework 8: Click Here.

Tutorial 8 (30/09/16): Look at your exam-manuscripts; discuss Homework 8; Quiz 8.

  • Week of October 3rd.

Lecture 15 (03/10/2016): Hom(V,W) is a vector space; End(V) is a ring; T : V --> V is injective iff Ker(T) = 0.

Lecture 16 (04/10/2016): Invertible linear transformations; isomorphisms; GL(V) is a group.

Homework 9: Click Here.

Tutorial 9 (07/10/2016) Discuss Homework 9; Quiz 9.

  • Week of October 10th. Mid-semester break.

  • Week of October 17th.

Lecture 17 (17/10/2016) Matrix of a linear transformation. Examples.

Lecture 18 (18/10/2016) Composition of transformations is same as multiplying their matrices; Similarity of matrices.

Homework 10: Click here.

Tutorial 10 (21/10/2016) Discuss Homework 10; Quiz 10.

Lecture 19 (21/10/2016) 9:00 to 10:00 a.m. in LHC 103. Determinants.

Lecture 20 (21/10/2016) 10:10 to 11:10 a.m. in LHC 101. Determinants, cont.

  • Week of October 24th.

No lectures this week.

Homework 11. Click here.

Tutorial 11 (28/10/2016). Discuss Homework 11; Quiz 11.

  • Week of October 31st.

Lecture 21 (31/10/2016) Eigenvalues, Eigenvectors, Eigenspace, Characteristic polynomials of a matrix/endomorphism.

Lecture 22 (01/11/2016) When can we diagonalize a matrix/endomorphism?

Homework 12. Click here.

Tutorial 12 (04/11/2016) Discuss Homework 12; Quiz 12.

  • Week of November 7th.

No Lecture on 07/11/2016. Watch the BBC documentary on Fermat's Last Theorem.

Lecture 23 (08/11/2016): Review of diagonalizability. Examples.

Homework 13. Click Here.

Tutorial 13 (11/11/2016) Discuss Homework 13; Quiz 13.

Lecture 24 (12/11/2016) 3:00 to 4:00 p.m. in LHC 103. Special make-up lecture. Inner products, Examples, Cauchy-Schwartz and Triangle inequalities.

  • Week of November 14th.

14/11/2016 is a Holiday--no lecture.

Lecture 25 (15/11/2016): Inner product spaces, orthogonal and orthonormal sets/bases, Gram-Schmidt Orthogonalization.

Homework 14. Click Here.

Lecture 26 (18/11/2016): at LHC 103, 9 a.m.; matrix of an inner product, orthogonal and unitary matrices.

Tutorial 14 (18/11/2016) Discuss Homework 14. There will be no Quiz during this last tutorial.

  • Week of November 21st.

Lecture 27 (21/11/2016): Review of the entire course.

  • Week of November 28th.

FINAL EXAM on 28/11/2016 from 10:00 am to 12 noon.