Mathematics 1104H/1104M/BIT1201A

Linear Algebra for Engineering or Science

My extra office before final exam will be on April 23, 2:30pm-4pm.

TA's names.

H1: Sabina Nketia. Office hours: Monday from 3:30 to 4:00pm at SA 517 and on Tuesday from 3:30pm to 4:00pm at the math tutorial center.

H2: Khan Hossein Shamsuttoha. Office hours: Tuesdays 3:30 to 4:30 in the Math tutorial center.

H3: Goldwyn Millar, Office hour: Wednesdays from 1 to 2 in the math tutorial centre.

H4: Abdulaziz Dahir. Office hour 11am-noon on Fridays at HP 3361

H5: Mary-Jean Harris. Office hour: 2:40 - 3:40 on Wednesday, math tutorial centre, HP 1160.

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

Topics covered in the class

Jan. 6: Introduction & system of linear equations.
Jan. 8: elementary row operations, Echelon forms, reduced row echelon forms.
Jan. 13: Solving system of linear equations; Vectors;.
Jan. 15: linear combination, veector equations, matrix equation.
Jan. 20: Solution sets of linear systems; linear independence.
Test #1 covers up to here.

Jan. 22: Linear transformation
Jan. 27: matrix of linear transformation; onto and one-to-one;
Jan. 29: onto and one-to-one; matrix operations.
Feb. 1: matrix multiplication, a game motivated by coding theory.
Feb. 3: invertible matrices(more properties, elementary matrices, find A^{-1})
Feb. 10: invertible matrix theorem, invertible linear transformations
Test #2 covers up to here.

Feb. 12. partitioned matrices, subpaces of R^n, column space and null space of A, basis.
Feb. 17-22 reading week.
Feb. 24. basis, coordinate vectors, the rank theorem.
Feb. 26. Determinants, properties
Mar. 3. Propertites of Determinants, Cramer's rule, Adjoints
Mar. 10. comments on determinants, Eigenvalues, Eigenvectors, Eigenspaces.
Test #3 covers up to here (Sections 2.8, 2.9, 3.1, 3.2, 3.3).

Mar. 12. Eigenvalues, Eigenvectors, diagonalization,
Mar. 17. More examples of diagonaliztion, google, complex numbers.
Mar. 19. polar form, De Moivre's theorem.
Mar. 24. complex eigenvalues and eigenvectors.
Mar. 26: inner product, length, and orthogonality.
Mar. 31: orthogonal set and orthogonal basis.
April 2: orthogonal projections, Gram-Schmidt process.
April 7: Gram-Schmidt process, review.

More suggested exercises:

Version 3.

Section 1.1: 1-16, 19-25.

Section 1.2: 1-22.

Section 1.3: 1-2, 5-6, 9-26.

Section 1.4: 1-26, 31-34.

Section 1.5: 1-15, 19, 21, 23-26, 29-34.

Section 1.7: 1-29, 33-40.

Test #1 covers up to here.

Section 1.8: 1-22, 33-36.

Section 1.9: 1-4, 15-36.

Section 2.1: 1-13, 15-34.

Section 2.2: 1-24, 29-35.

Section 2.3: 1-40.

Test #2 covers up to here. -->

Section 2.4: 1-10, 25.

Section 2.8: 1-30.

Section 2.9: 1-27.

Section 3.1: 1-41.

Section 3.2: 1-43.

Section 3.3; 1-16, 19, 23, 26, 27, 29.

Test #3 covers up to here.

Section 5.1: 1-22, 25-30.

Section 5.2: 1-17, 21-22.

Section 5.3: 1-32.

Section 5.5: 1, 3, 13, 15, 23

Section 6.1: 1-31.

Section 6.2: 1-24.

Section 6.3: 1-12, 17, 18, 21, 22.

Section 6.4: 1-12.

Version 4