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 short tests will be established at a later date.

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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
   • Concept of Matrices
   • Operations on matrices
   • Multiplication of matrices
   • Powers of matrix
   • Rank theorem
3. Factoring matrices
   • System of linear equations
   • Factoring matrices
   • Problems
4. System of linear equations
   • Solution of homogeneous linear system of equations
   • Solution of nonhomogeneous linear system of equations
5. The concept of the inverse matrix
   • Matrix equations
   • Inverse matrix
6. Quadratic forms
   • Definition of quadratic froms
   • 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
   • 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
   • 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