APPLICATION OF MATRICES TO REAL LIFE PROBLEMS
CHAPTER ONE
INTRODUCTION AND LITERATURE REVIEW
INTRODUCTION
This research is divided into five chapters. The first chapter provides context for the study, as well as the research problem and hypotheses for testing. The second chapter is organized to provide a literature review for the study. This review is organized into three sections: theoretical framework, empirical framework, and conceptual framework. The third chapter discusses research methodology, which includes the research design, sampling method, data collection, and research instruments used. Chapter four aims to analyze the results; it also includes a detailed analysis of the data collected and information presentation using quantitative and statistical models. The summary, conclusion, and recommendation are all covered in the fifth chapter. the calculation of battery power outputs and resistor conversion of electrical energy into another useful energy.
Matrices play an important role in the realistic appearance of motion created by projecting three-dimensional images into a two-dimensional screen. Matrices are used in Economics to calculate gross domestic products, which aids in the efficient calculation of goods production.
Matrices serve as the foundation for robot movement. Robot movements are programmed using matrices with row and column calculations. The inputs for controlling robots are based on matrices calculations. Matrices are also used by scientists in many organizations to record data from their experiments.
HISTORY OF MATRICES
Matrix history dates back to antiquity, but the term “matrix” was not applied to the concept until 1850. The term matrix is derived from the Latin word for womb, and it retains that meaning in English. It can also refer to any location where something is formed or produced more broadly.
The study of simultaneous linear equations gave rise to mathematical matrices. The first known example of the use of the matrix method to solve simultaneous equations is found in an important text of the mathematical Art Chiu Chang SuanShu. The concept of determinant first appeared nearly two millennia before its alleged invention in 1683 by Japanese mathematician Seki Kowa or his German contemporaries Godfried Leibnitz.
The origins of matrices and determinants can be traced back to the The 2nd century BC, with traces dating back to the 4th century BC. However, it wasn’t until the end of the 17th century that the ideas reappeared and real development began. The study of systems of linear equations led to the development of matrices. The Babylonians first began studying problems that led to simultaneous linear equations, and some of these have survived on clay tablets.
Between 200BC and 100BC, the Chinese came much closer to matrices than the Babylonians. Indeed, the nine-chapter text on Mathematical Art written during the Han Dynasty provides the first known example of matrix methods. One approach is what is now known as the Gaussian Elimination. method (which is a method used to solve simultaneous linear equations) (which is a method used to solve simultaneous linear equations). This method was not widely used by mathematicians until the nineteenth century. The matrix theory was the result of a fifty-year study of Co-efficient systems of quadratic forms by a man named Leibniz. Many common manipulations of uncomplicated matrix theory appeared long before matrices were studied mathematically.
Gauss first began to describe matrix multiplication (which he thinks of as a number organization, so he had not yet reached the concept of matrix algebra) and the inverse of a matrix in the context of the collection of quadratic form coefficients. Between 1803 and 1809, Gauss worked on the study of Asteroid Pallas and obtained a Six linear equations with six unknowns form a system. Gauss developed a systematic method for solving such equations, known as the Gaussian elimination method on the coefficient matrix. In an 1812 paper, the multiplication theorem was proven and published for the first time.
In 1844, Eisenstein used a single letter to represent linear substitutions and demonstrated how to add and multiply them like ordinary numbers. It is reasonable to believe that Eisenstein was the first to consider linear substitutions. After Leibniz’ use of determinant, Cramer presented his determinant-based formula for solving systems of linear equations, which is now known as “Cramer’s rule,” in 1750.
Sylvester was the first to use the term “matrix” in 1850. Sylvester defined a matrix as an oblong shape. term arrangement and saw it as something that led to various determinants from square assortment contained within it. Cayley was the first person to publish a note on the inverse of a matrix in 1853. Cayley used addition, multiplication, scalar multiplication, and inverses to define the matrix algebraically. He provided a detailed explanation of a matrix’s inverse. Subtraction came soon after using matrices for addition, multiplication, and inverses.
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