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### Linear algebra 1

 Code: 21501 ECTS: 8.0 Lecturers in charge: prof. dr. sc. Ljiljana Arambašić - Lectures prof. dr. sc. Damir Bakić - Lectures Lecturers: doc. dr. sc. Igor Ciganović - Exercises Matko Grbac, mag. math. - Exercises Mateo Tomašević, mag. math. - Exercises English level: 1,0,0 All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.

### 1. komponenta

Lecture typeTotal
Lectures 45
Exercises 60
Description:
COURSE AIMS AND OBJECTIVES: Introduction to finite dimensional vector spaces. Basic notions on linear independence, bases, subspaces, matrices, inverses, determinant.

COURSE DESCRIPTION AND SYLLABUS:
1. Opearions with vectors, addition and scalar multiplication. Colinear an coplanar vectors. Linear combinations, linear independence. Rotations, reflections, orthogonal projections.
2. Linear systems. Solution of linear system. Geometry of the solution set. Matrix form of linear systems. matrices. Eliminations of unknowns as LU factorisation of the coefficient matrix. Determinant of matrices.
3. Linearn systems . Geometry of the solution set. Equivalent systems. Elementary transformations and LU factorization. Matrix form of linear system. Homogeneous systems.
4. Homogeneous systems - structure of the solution set. Linear combination. Matrices: matrices, addition and multiplication of matrices. Vector space Rn.
5. Group. Field. Vector space. Linear independence. Basis. Dimension of vector space. Finite dimensional vector space. Representation of vectors in given basis. Examples of vector spaces.
6. Subspace. Intersection and sum of subspaces.
7. Determinant. Binet - Cauchy theorem. Permutations.
8. Rank of matrix. Elementary transformations. Inverse matrix.
9. Linear systems . Structure of the solution set. Linear manifold. Gauss eliminations. LU factorization.
10. Vector space V3. Vectors as equivalence classes. Addition and scalar multiplication. Basis. Scalar product. Orthonormal basis. Orthogonal projection. Cross product. Mixed product.
Literature:
1. K. Horvatić: Linearna algebra
2. N. Bakić, A. Milas: Zbirka zadataka iz linearne algebre
3. G. Strang: Linear algebra and its applications
4. N. Elezović: Linearna algebra
 1. semester Mandatory course - Regular study - Mathematics
Consultations schedule:

### Content

Link to the course (former) web page: https://web.math.pmf.unizg.hr/nastava/la1/

Link to the notices web page: http://www.pmf.unizg.hr/math/predmet/linalg1