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Lecture — The Basics of Matrix Algebra’ Matrix (or linear) algebra provides a convenient methodology for finding solutions to a system of simultaneous Jinear equations. Many economic relationships can be approximated by linear equations or converted to linear relationships via appropriate transformations (e.g. log linearization). This lecture will demonstrate the various matrix operations, how to solve a system of equations employing matrices as well as highlight a few special determinants and matrices. 1. The Fundamentals 1.1 Terminology e A matrix is a rectangular array of numbers, parameters. or variables, each of which has a carefully ordered place within the matrix. © The numbers, parameters or variables are referred to as elements of the matrix. A generic element of a matrix has a specific address identified by its subscript: a, is the element in the #” row and j” column of a matrix. * The numbers in a horizontal line are called rows; the numbers ina vertica) line are called columns. « The number of rows r and columns ¢ defines the dimensions of the matrix ("xe yor by c”. The row number always precedes the column number. A matrix that has an equal number of rows and columns is called a square matrix A matrix with a single column (ie. with dimensions r x1) is called a column vector A matrix with a single row (i.e. with dimensions 1c} is called a row vector. ‘A matrix which converts the rows of A to columns and columns of A to rows is called the transpose of A and is designated by A‘or A’. eee 1.2 Addition and Subtraction of Matrices Addition (and subtraction) of two matrices A+B (or A—B) requires that the matrices be of equal dimensions. Each element of the one matrix is then added to (subtracted from) the corresponding element of the other matrix. Example 1: (® 9 7) 1 3 °) 8+1 943 746 (9 12 13) A=\3 6 2 B=|5 2 4 A+B=|345 642 244} =[|8 8 6 la 5 io), 79 2). [447 5-9 10+2),, Ul 14 12s 1.3 Scalar Multiplication Multiplication of a matrix by a number or scalar involves multiplication of every element of the matrix by that number (ie. scaling the matrix up or down by the magnitude of that number), _ ' The material for this lecture is sourced from Dowling, 
