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# APPLICATION OF MATRICES TO INPUT AND OUTPUT MODEL AND PRICE DETERMINATION

**APPLICATION OF MATRICES TO INPUT AND OUTPUT MODEL AND PRICE DETERMINATION**

**CHAPTER ONE**

**1.1 INTRODUCTION**

Several aspects of life or fields are characterized by system which in most cases are complex and require rigorous analysis to be able to solve the problems posed by these systems. The importance of matrix cannot be overemphasized as it has been a tool for the simplification complex system in order to obtain solutions. However, in this project work, we are taking specific consideration of examples from input-output model and on price determination.

In chapter one, we will consider the introduction of matrix with regards to this project work. We are giving to be defining important terms that are relevant and will and proper understanding of the work.

Chapter two, focuses on matrix concepts. These concepts will be useful in its application to solving problems from input-output model & price determination. The chapter two, of this work talk about a model (Leontief input-output Model) that uses matrix concepts to solve problems especially from Economics. We will see how Leontief used matrix to model the production level of a nation’s Economy.

Chapter Three, will focus on different applications of matrices. Application would be drawn from input-output model & price determination and be solved using matrix approach. Chapter four, on interpretation of result of chapter three and what we have been able to achieve in the project work. Details

**1.2 OBJECTIVE OF THE STUDY**

Mathematics has been known for its operations or uses for numbers. This project work will showcase the generosity of mathematics to other disciplines using problems from input-output model and on price determination as a case study.

Matrix which is the arrangement of numbers in rows and columns plays a huge role in solving most economical problems. Therefore, the sole objective of this study is to actually show how matrix can be useful in solving problems from input and output model and on price determination. This will significantly show practical application of matrices.

**1.3 SIGNIFICANCE OF THE STUDY**

- To provide a solid foundation in the mathematics of matrix.
- To discuss vital application, so that students may know where and how matrix is applied to national economy i.e. real life situation.
- Finally, we shall look at the application of matrices in prices determination and Leontief input-output model in economics.

**1.4 SCOPE OF THE STUDY**

The methodology here, is to define or establish some basic matrix concept which will be useful in solving problem in chapter three of this project topic, problems which have their base in Business and Economics will perhaps be solved by the use of matrix concept.

**1.5 DEFINITION OF MATRIX**

A matrix is a rectangular array of numbers or other mathematical objects for which operation such as addition and multiplicatio are defined. Most commonly, a matrix over a field F is a rectangular array of scalars

from F.

A= a_{11} a_{22}

a_{21} a_{22}

The numbers, symbols or expression in the matrix are called its entries or its element. The horizontal and vertical lines in matrix are called rows and columns respectively. The size of a matrix is defined by the number of rows and columns it contains. A matrix with m rows and n columns is called an m x n matrix or m by n matrix, while m and n are called its dimension.

**1.6. Types of Matrices**

Matrices can be classified in several ways. Some of these classifications are based on symmetry, sparcity, dimensions etc. We have different types of matrix such as symmetric, anti-symmetric, null matrix (All entries are zero),Identity matrix, square matrix, rectangular matrix, column and row matrix diagonal, upper and lower triangular matrix invertible matrix etc. some of these matrices will be given formal definition in chapter two.

**1.7. Important definitions**

**1.7.1 Economics: **This is the social science concerned with the production and consumption of goods and services, and the analysis of the commercial of activities of a society.

1.7.2 **Business: **A business (also known as enterprise or firm) is an organization involve in the trade of goods, services or both to consumers.

**1.7.3 Input-output matrix:** This is a representation or regional economic accounting that records the ways industries trade with one another, as well as to produce for consumption and investments.