A matrix is a rectangular array of numbers. The numbers in the array are called the entries in the matrix. We use the capital letters to denote matrices such as A, B, C,. The size of matrix is described in terms of the number of rows and columns it contains. | Example 1: The following rectangular array describes the profit (milions dollar) of 3 branches in 5 years: 2008 2009 2010 2011 2012 I 300 420 360 450 600 II 310 250 300 210 340 III 600 630 670 610 700 Module 1: MATRIX Duy Tân University Lecturer: Thân Thị Quỳnh Dao Natural Science Department Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix 1. Definition - A matrix is a rectangular array of numbers. The numbers in the array are called the entries in the matrix. 300 420 360 450 600 310 250 300 210 340 600 630 670 610 700 300 420 360 450 600 310 250 300 210 340 600 630 670 610 700 1. Definition - A matrix is a rectangular array of numbers. The numbers in the array are called the entries in the matrix. - We use the capital letters to denote matrices such as A, B, C . - The size of matrix is described in terms of the number of rows and columns it contains. 300 420 360 450 600 310 250 300 210 340 600 630 670 610 700 1. Definition - Let m,n are positive integers. A general mxn matrix is a rectangular array of number with m rows and n columns as the entry occurs in row i and column j. Example: 2. Some special matrices - Row-matrix: A matrix with only 1 row. A general row matrix would be written as - Column-matrix: A matrix with only 1 column. A general column matrix would be written as or or 2. Some special matrices - Square matrix of order n: A matrix with n rows, n columns. A general square matrix of order n would be written as or main diagonal of A. 2. Some special matrices - Matrix unit of order n: A square matrix of order n whose all entris on the main diagonal are 1 and the others are 0. A general matrix unit of order n would be written as 2. Some special matrices - Zero matrix: a matrix, all of whose entries are zero, is called zero matrix. 3. Operations on matrices - Two matrices are defined to be equal if they have the same size and the corresponding entries are equal. Example: Find x such that A = B, B = C? 3. Operations on matrices - Transposition: Let A is any mxn matrix, the transpose of A, denoted by is defined to be the nxm matrix that results from interchanging the rows and the columns of A. 3. Operations on matrices - Addition and subtraction: Example: Find (if any): A + B, A – B, B + C? 3. Operations on matrices - Scalar multiples: let c is real number Example: Find 3A? Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department 3. Operations on matrices Example: Find: 2A + 3B – I3 , with: Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department 3. Operations on matrices - Multiplying matrices: Example: Find AB? ; Thank you for your attention Natural Science Department
