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2023 | OriginalPaper | Chapter

10. Matrices and Determinants

Authors : Vassilis C. Mavron, Timothy N. Phillips

Published in: Elements of Mathematics for Economics and Finance

Publisher: Springer International Publishing

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Abstract

Matrix theory is a powerful mathematical tool for dealing with data as a whole rather than the individual items of data. Matrices are especially useful in the theory of equations. They can be used to solve systems of simultaneous linear equations. Determinants are related to matrices and are useful for determining whether or not a unique solution exists. In some cases, using determinants, the solution for each unknown can be expressed explicitly in terms of the coefficients of the equations by applying what is known as Cramer’s rule. Systems of simultaneous linear equations occur, for example, when optimizing a function using Lagrange multipliers or when trying to find the equilibrium prices of interdependent commodities. As we shall see, matrices can be added and in some cases multiplied together. In economics, business, and finance, many basic theoretical models are linear in that they are described in some way by linear functions. Analyzing these models is made simpler by matrix algebra.

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Metadata
Title
Matrices and Determinants
Authors
Vassilis C. Mavron
Timothy N. Phillips
Copyright Year
2023
DOI
https://doi.org/10.1007/978-3-031-43910-0_10

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