for the Fall semester of 2025-2026.

The Linear Algebra classes of Mathematics I – ADIN001NABB.

Important information

• The Office Hours is in S 208/b at Monday 15.30. Registration via e-mail is required not later than 7pm of the actual day before.
• Attendance is compulsory in the classes.
• The precise schedule of the quizzes: Week 3 (September 29) Week 6 (October 20) Week 9 (November 17) Week 12 (December 8)

The expected date of the first written midterm is December 16. Two additional major written tests will take place during the first two weeks of the new year.

No rescheduling or make-up opportunities will be provided for the mini quizzes.

The written examination is scheduled for the very first week of the examination period. Attendance is compulsory for all students.

Grading

• Each of the four mini quizzes is worth a maximum of 5 points. The best three results will be counted, contributing up to 15 points.
• The final written exam is worth 25 points.
• Altogether, a maximum of 40 points can be earned from the written components of the course.
• Optional oral examinations are available during the examination period.

All regulations and conditions are governed by the University’s Code of Studies and Examinations.

Weekly Schedule

The week-by-week schedule is as follows:

1. Elements of Linear Algebra download
   • Vectors
   • Linear Combination
   • Basis
   • Basis transformation
   • Applications
2. Matrix
   • Inner product download
   • Concept of Matrices
   • Operations on matrices
   • Multiplication of matrices
   • Powers of matrix
   • Rank theorem
3. Factoring matrices download
   • System of linear equations
   • Factoring matrices
   • Rank–Nullity theorem
   • Problems
4. System of linear equations download
   • Solution of homogeneous linear system of equations
   • Solution of nonhomogeneous linear system of equations
5. The concept of the inverse matrix download
   • Matrix equations
   • Inverse matrix
6. Quadratic forms
   • Definition of quadratic froms download
   • Dyadic decomposition
     • Dyad is the matrix of a complete square
     • High school method for small size
     • Professional method with Gaussian Elimination
   • Problems
   • Definiteness of a quadratic form
   • Summary
7. Determinant download
   • Parity of permutations
   • The concept of determinant
   • Special cases when the size is 1,2, or 3
   • Properties
   • Compute the determinnant using Gauss-Jordan elimination
   • Expension by minors
   • Characteristic polynomial
8. Diagonalize a matrix download
   • Concept of eigenvalue and eigenvector
   • The G-J elimination to find the eigenvalues and the eigenvectors.
   • Diagonalizable matrices.
   • Problems
9. Preparation for the final exam
   • Mock exam