Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department Example 1: The following rectangular array describes the profit (milions dollar) of 3 branches in 5 years: I II III
Company LOGO 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
Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department 1. Definition - A matrix is a rectangular array of numbers. The numbers in the array are called the entries in the matrix.
Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department
Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department
Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department 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.
Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department
Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department 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.
Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department Example:
Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department
Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department 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
Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department
Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department
Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department 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.
Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department
Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department
Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department 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
Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department 2. Some special matrices - Zero matrix: a matrix, all of whose entries are zero, is called zero matrix.
Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department 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?
Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department 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.
Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department 3. Operations on matrices - Addition and subtraction: Example: Find (if any): A + B, A – B, B + C?
Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department 3. Operations on matrices - Scalar multiples: let c is real number Example: Find 3A?
Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department 3. Operations on matrices Example: Find: 2A + 3B – I 3, with:
Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department 3. Operations on matrices - Multiplying matrices: Example: Find AB?
Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department ;