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Primjene determinanti
Vesna Biuk (2019)
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Applied Mathematics
Applied Mathematics Research Group
Cite this document

Biuk, V. (2019). Primjene determinanti (Undergraduate thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:888452

Biuk, Vesna. "Primjene determinanti." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:888452

Biuk, Vesna. "Primjene determinanti." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:888452

Biuk, V. (2019). 'Primjene determinanti', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 25 February 2020, https://urn.nsk.hr/urn:nbn:hr:126:888452

Biuk V. Primjene determinanti [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2019 [cited 2020 February 25] Available at: https://urn.nsk.hr/urn:nbn:hr:126:888452

V. Biuk, "Primjene determinanti", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:126:888452

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Metadata
TitlePrimjene determinanti
Title (english)Applications of Determinants
AuthorVesna Biuk
MentorDarija Marković (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Applied Mathematics)
(Applied Mathematics Research Group)
Osijek
Defense date and country2019-09-30, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Algebra
Abstract
Tema ovog rada su primjene determinanti matrica. Najprije ćemo nabrojati osnovna svojstva i teoreme koji opisuju determinante, a koji će nam biti potrebni u kasnijim računima i dokazima. Zatim ćemo govoriti o raznim primjenama determinanti. Definirat ćemo adjunktu matrice te pomoću nje i determinante matrice izvesti i dokazati formulu za pronalaženje inverza matrice. Nakon toga, govorit ćemo o Cramerovoj metodi za rješavanje sustava linearnih jednadžbi te o određivanju svojstvenog polinoma i rješavanju svojstvenog problema. Govorit ćemo i o primjeni determinante za određivanje zajedničkog korijena dvaju polinoma te također o primjenama determinanti u analitičkoj geometriji. Tu ćemo se dotaknuti površine trokuta i paralelograma te volumena tetraedra i paralelopipeda. Također, pomoću determinanti odredit ćemo jednadžbu pravca, ravnine i sfere. Na kraju ćemo definirati osnovne pojmove iz teorije grafova i objasniti primjenu determinanti u tom području.
Abstract (english)
The subject of this paper is the application of the determinants of matrix. First, we will state the basic properties and theorems that describe the determinants, which will be needed in later calculations and proofs. Then we will talk about various application of determinants. We will define the adjoint of a matrix. With use of it and determinant of the matrix we will derive and prove the formula for finding the inverse of matrix. After that, we will talk about Cramer’s method for solving the linear system and determining its characteristic polynomial and solving its eigenvalue problem. We will also discuss the application of determinants for determing the common roots of two polynomials and the application of determinants in analytical geometry. Here we will mention the surfaces of triangles and parallelograms and the volume of tetrahedron and parallelepipeds. Also, we use the determinants to determine the equation of the line, plane and sphere. Finally, we will define the basic concepts from graph theory and explain the application of determinants to them.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:888452
Study programmeTitle: University undergraduate study programme in mathematics
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
Created on2019-10-21 07:02:11