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# VARIOUS APPLICATIONS OF LINEAR ALGEBRA

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```									               VARIOUS APPLICATIONS OF LINEAR ALGEBRA
H.A. Parhusip
Satya Wacana Christian University
Jl. Diponegoro 55 -60 Salatiga 50711
hannaariniparhusip@yahoo.co.id

ABSTRACT
Various applications of linear algebra are presented here. Undergraduate students in mathematics are
mainly have no enough background in integrating linear algebra from different subjects and have difficulties to
deal with data for applying linear algebra. On the other hand, students have learnt many properties in linear
algebra but students are lacking to work with in practical sense. Therefore this paper shows some guidelines to
handle this problem through some examples taken from some researchs on linear algebra by using data from
surrounding.
Multivariate regression is introduced which is used to fit closing stock prices as an example. QR
decomposition is recalled in order to solve a linear system with no solution in the classical linear algebra
lectures.
Modelling on stevioside with a two dimensional quadratic function, logistic model of crown diameter
of Kailan, discriminant analysis of foods, protein content of beans, Belousov-Zhabotinsky (BZ) reaction as a
model on differential equations are some examples shown on this paper. These applications are mainly dealt
with parameters determination that lead to linear system and nonlinear system. Least square and Newton
method are the basic used methods in this paper which are solved by fmincon and lsqnonlin and provided by
MATLAB. One needs to know a particular software language (such as MATLAB, R) to reinvent the results in
this paper.

Keywords: least square, positive definite, convex-nonconvex functions,discriminant analysis, matrix
covariance, eigenvalues-eigenvectors.

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