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.