matrix_adj - ECON1003 Mathematics for the Social Sciences...

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1 ECON1003 Mathematics for the Social Sciences Topic 5: Matrix Algebra Lecturer: Marlon Tracey
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2 Objective o At the end of this topic, students should be able to: o Do operations on matrices. o Determine the determinant and inverse of a matrix. o Identify the properties of the inverse. o Solve a given system of equations using matrix inversion and Cramer’s rule.
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3 Outline o Introduction o Definition of a matrix o Types of matrices o Matrix addition and subtraction o Multiplication and transposition o The determinant of a 2 x 2 and a 3 x 3 matrices. o The inverse of a 2 x 2. o Matrix solution of 2 x 2 and 3 x 3 systems of linear equations.
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4 Introduction o Matrices are useful to solving large complex linear simultaneous equations that involves a large number of unknowns. In these cases, using the methods of elimination or substitution can become quite tedious and time consuming. o First we need know the terminologies and manipulations of matrices and then we will be equipped to solve these complex systems.
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5 Definition of a matrix o A matrix is a rectangular array (an orderly arrangement) of values defined in terms of a specific number of rows and a specific number of columns. For example, o Each of the statements in bold below the matrices are referred to as the order of the matrix (dimension). The first value represents the number of rows and the second value represents the number of columns. We use capital letters denote a matrix (for e.g. A, B etc.). = 1 4 4 5 3 2 A 3 x 2 = 5 3 8 2 B 2 x 2 = 5 4 3 2 4 5 4 1 7 C 3 x 3
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6 Types of matrix I o Row matrix :- A matrix with only a single row of elements. E.g. (2 5). o Column matrix :- A matrix with only a single column of elements. E.g. o Square matrix :- A matrix which has the same number of rows and columns. E.g. o Equal matrices :- Two matrices are equal if the order of the matrices and corresponding elements of the matrices are equal. E.g. 3
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This note was uploaded on 03/16/2011 for the course ECON 1003 taught by Professor Dr.mcdonald during the Spring '11 term at University of the West Indies at Mona.

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matrix_adj - ECON1003 Mathematics for the Social Sciences...

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