Interpretación geométrica de la regla de Cramer

Authors

  • Juan Carlos Bressan
  • Ana E. Ferrazzi de Bressan

DOI:

https://doi.org/10.54343/reiec.v3i1.332

Keywords:

Knowing kernel, Cramer rule, linear transformation, determinant, orthogonal

Abstract

The knowing kernel of this work is Cramer rule, its relations with linear transformations and its geometric interpretation. To obtain it, this paper was organized in two parts. 

Part one: It was made a geometric interpretation and demonstration of Cramer rule for systems of three linear equations, using vector and inner products and Euclidean space properties. Part two: It was generalized that concepts at systems of n-linear equations using Linear Algebra properties. 

In both parts, it was expressed the unknown quantities as orthogonal components quotient with its interpretations. Almost, it was analyzed the linear system solutions when the vector columns coefficient of every unknown quantities are orthogonal or ortonormal two.

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References

Burgos, J. (1993). Álgebra lineal, McGraw-Hill.

Ferrazzi de Bressan, A. y Bressan, J. (1997). Nociones de trigonometría y vectores, Cuadernos UADE 88, Universidad Argentina de la Empresa.

Kolman, B. y HILL, D. (2006). Álgebra lineal, Pearson Educación, Prentice-Hall.

Lakatos, I. Pruebas y refutaciones. La lógica del descubrimiento matemático, Alianza Editorial Santaló, L. (1961). Vectores y tensores con sus aplicaciones, Editorial Universitaria de Buenos Aires. Santaló, L. (1968), Espacios vectoriales y geometría analítica, Serie de Matemática, Departamento de Asuntos Científicos, Unión Panamericana, Secretaria General de la OEA.

Published

2008-09-02

Issue

Section

Articles