(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**

Read

4.4 Eigenvalues and eigenvectors

8.2 Similarity and diagonalizability

**Solution to Assignment 2**

**Assignment 3 [skip Question 3(c)]**

Read

8.8 Complex eigenvalues and eigenvectors

Appendix B Complex numbers

**Solution to Assignment 3**

**Assignment 4**

Read

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**

Read

7.8 Best approximation and least squares

7.10 QR-decomposition; (skip Householder transformations)

**Solution to Assignment 5**

**Assignment 6**

Read

8.10 Systems of differential equations

8.3,8.9 Orthogonal diagonalizabilty

**Solution to Assignment 6**

**Assignment 7**

Read

8.4 Quadratic forms

8.5 Application of quadratic forms to optimization

**Solution to Assignment 7**

**Assignment 8**

Read

9.1 Vector space axioms

7.1 to 7.5

7.11 Coordinates with respect to a basis

**Solution to Assignment 8**

**Assignment 9**

Read

9.2 Inner product space. Fourier Series

9.3 General linear transformation

8.1 Matrix representation of linear transformation

**Solution to Assignment 9**

**Assignment 10**

Read

8.6 Singular value decomposition

3.8 Partitioned matrices

8.7 The pseudoinverse

**Solution to Assignment 10**