# Weekly Homework Assignments

(Assignments are not to be handed in)

Assignment 1
Review the material in
Chapter 1 - Sections 1.1 to 1.3: Vectors
Chapter 2 - Sections 2.1 to 2.3: System of linear equations
Chapter 3 - Sections 3.1 to 3.6: Matrices and matrix algebra
Chapter 4 - Sections 4.1 to 4.4: Determinants
Chapter 6 - Sections 6.1 to 6.4: Linear transformations
Chapter 7 - Sections 7.1 to 7.5: Dimension and structure
of Anton and Busby's book.
Solution to Assignment 1

Assignment 2
4.4 Eigenvalues and eigenvectors
8.2 Similarity and diagonalizability
Solution to Assignment 2

Assignment 3 [skip Question 3(c)]
8.8 Complex eigenvalues and eigenvectors
Appendix B Complex numbers
Solution to Assignment 3

Assignment 4
7.7 Projection theorem and its implications
7.9 Orthonormal bases and the Gram-Schmidt process
6.2 Geometry of linear operators
Solution to Assignment 4

Assignment 5
7.8 Best approximation and least squares
7.10 QR-decomposition; (skip Householder transformations)
Solution to Assignment 5

Assignment 6
8.10 Systems of differential equations
8.3,8.9 Orthogonal diagonalizabilty
Solution to Assignment 6

Assignment 7
8.5 Application of quadratic forms to optimization
Solution to Assignment 7

Assignment 8
9.1 Vector space axioms
7.1 to 7.5
7.11 Coordinates with respect to a basis
Solution to Assignment 8

Assignment 9