# Guidelines for the first long exam

### What to bring

1. Blue book
2. Pens
3. Clean scratch papers (optional, you can write your solutions on the blue book)

### Coverage and Competencies

#### Asymptotic Analysis

1. Evaluating asymptotic relationships based on graphs
2. Evaluating asymptotic relationships based on asymptotic notation properties
3. Reducing complex functions to representative functions
4. Understanding the applications of asymptotic notation in algorithm analysis

#### Introduction to Linear Algebra

1. Understanding the relationships of Linear algebra concepts and matrices
2. Finding the transformation matrix based on graphs
3. Finding the determinants of 2-dimensional transformations
4. Finding the determinants of 3-dimensional transformations
5. Understanding linearly dependent basis vectors
6. Finding transformation matrix based on the described distortion
7. Understanding the meaning of the determinant value
8. Transforming vectors based on arbitrary matrices
9. Applying composed transformations on vectors
10. Undoing transformations using the inverse matrix
11. Finding the inverse of a transformation
12. Understanding non-square transformations
13. Understanding the properties of singular matrices
14. Finding eigenvectors and eigenvalues of some transformation
15. Checking if a given vector is an eigenvector of some transformation
16. Finding the eigenvalue of a given eigenvector
17. Finding the dot products of given vectors
18. Understanding the meaning of a dot product value.

### Exam Type

- Multiple choice, 23-items, 31 total points