# Matrices and Linear Equations

May 19th, 2015
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2.1 Introduction : Matrices and Linear Equations made their appearance long time ago. The word ‘matrix’ was first introduced by Sylvester(1850). Many of the symbols and operations that we used today were formalized by Cayley(1841). In the present day, we use matrices to solve many complex problems of very great importance in Medical Diagnostic Systems, Public Transport System, Communication Network and others.

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UNIT 2MATRICES2.1 IntroductionMatrices and Linear Equations made their appearance long time ago. The wordmatrix was first introduced by Sylvester(1850). Many of the symbols andoperations that we used today were formalized by Cayley(1841). In the presentday, we use matrices to solve many complex problems of very great importance inMedical Diagnostic Systems, Public Transport System, Communication Networkand others. In this topic students will be exposed to the operations of matrices,determine the inverse matrices and hence solve the system of linear equation byusing the matrices.ObjectivesAt the end of the topic, students should be able to: State the size of matrices according to the number of rows and columns. Perform the algebraic operation on matrices for 2 and 3 rows matrices. Recognize matrices according to their types . Determine the inverse matrix by determinant and adjoin method for 3 by 3matrices. Solve the system of linear equation using the inverse matrix method and theCramers rule for 3 by 3 matrices.392.2Definition of Matrices2.2.1 Size and SymbolMatrices have columns and rows.1 2Let A 3 4Column1row 1row 2Column2A symbol of a matrix can be written as :() or[]2.2.2 Element of MatricesEach number in a matrix is called the element of the matrix.1 2If A ,3 4so numbers like 1, 2, 3, and 4 are the elements of matrix A.2.2.3 Size of a Mat

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