The research work is solely aimed at solving ystem of linear equation is a different way. System of solving linear equation may result into rectangular Augmented matrix or square Augmented matrix. The methods used this research work has led to a new way or technique in solving system of linear equation – be it in the rectangular or square Augmented matrix form. Most pairs of simultaneous linear equations are usually represented by square augmented matrices with unknown variables, usually 2 x 2 and 3 x 3 matrices.
From this research work, it is now possible to:
a. Solve simultaneous equations arising from rectangular Augmented matrix of 3 x 2 and 4 x2 order
b. Find the determinant of 2 x 2 and 3 x 3 with a different method – that never existed before.
c. Solve 2 x 2 and 3 x 3 and 4 x 4 aquare Augmented matrix with a new method using determinant but quite different from that of crammer’s rule or method.
Inhaltsverzeichnis (Table of Contents)
- INTRODUCTION
- 1.1
- 1.2
- EHIMETALOR'S FORMULA FOR SOLVING 3 X 2 AUGMENTED MATRIX WITH THREE UNKNOWN VARIABLES.
- Case 1:
- Case 2:
- Case 3:
- WORKED EXAMPLE
Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)
This research work aims to introduce a new method for solving systems of linear equations, particularly those involving rectangular augmented matrices. The new technique, referred to as "Ehimetalor's formula," offers a way to solve these equations with a different approach than traditional methods.
- Solving simultaneous linear equations with rectangular augmented matrices
- Developing new formulas for solving specific matrix orders (3 x 2, 4 x 2)
- Introducing a new method for calculating determinants
- Presenting an alternative approach to solving systems of linear equations using determinants
- Comparing the new method to existing methods like Cramer's rule and Gaussian elimination
Zusammenfassung der Kapitel (Chapter Summaries)
- INTRODUCTION: This chapter outlines the challenges associated with solving simultaneous linear equations with rectangular augmented matrices. It highlights the lack of standardized methods for such equations and introduces the research's focus on developing new solutions for specific matrix orders (3 x 2 and 4 x 2).
- EHIMETALOR'S FORMULA FOR SOLVING 3 X 2 AUGMENTED MATRIX WITH THREE UNKNOWN VARIABLES.: This chapter presents the core of the research, outlining the new formula developed for solving systems of linear equations with a 3 x 2 rectangular augmented matrix. It provides a step-by-step explanation of the formula and its application through different cases. Each case involves a specific scenario and demonstrates how the formula can be utilized to solve the equations.
- WORKED EXAMPLE: This chapter provides a practical example of how to apply the newly developed formula to solve a system of simultaneous equations. The example illustrates the steps involved in the process and demonstrates the efficacy of the formula in arriving at the solution.
Schlüsselwörter (Keywords)
The main focus of this research revolves around solving systems of simultaneous linear equations, specifically those represented by rectangular augmented matrices. Key terms include: simultaneous equations, linear equations, rectangular augmented matrix, square augmented matrix, unknown variables, solving equations, solving linear equations, determinants, and Cramer's rule.
Frequently Asked Questions
What is Ehimetalor's Formula?
It is a new mathematical method developed to solve systems of linear equations, specifically for rectangular augmented matrices of 3x2 and 4x2 order.
How does this method differ from Cramer's Rule?
While it uses determinants, it provides a different technique that can handle non-square (rectangular) augmented matrices where traditional rules might fail.
Can this formula find determinants for 3x3 matrices?
Yes, the research introduces a new method for calculating determinants of 2x2 and 3x3 matrices that did not exist before.
What is an augmented matrix?
A matrix used in linear algebra to represent a system of linear equations, combining the coefficients and the constant terms.
What are the practical applications of this new solving technique?
It offers more flexibility in solving simultaneous equations with a different number of variables and equations than standard methods.
- Quote paper
- H. Ehimetalor (Author), 2023, Simultaneous Linear Equations Journal. New Method of Solving, Munich, GRIN Verlag, https://www.grin.com/document/1380026
