Chapter 1: Matrix, Determinant, System of linear equations - Module 1: Matrix

- Transposition: Let A is any mxn matrix, the transpose of A, denoted by AT is defined to be the nxm matrix that results from interchanging the rows and the columns of A.

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Example 1: The following rectangular array describes the profit (milions dollar) of 3 branches in 5 years:20082009201020112012I300420360450600II310250300210340III600630670610700Module 1:MATRIXDuy Tân UniversityLecturer: Thân Thị Quỳnh DaoNatural Science DepartmentChapter 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.3004203604506003102503002103406006306706107003004203604506003102503002103406006306706107001. 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.3004203604506003102503002103406006306706107001. 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 oror2. 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 asormain 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 as2. 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 byis 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 Department3. Operations on matrices Example: Find: 2A + 3B – I3 , with: Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department3. Operations on matrices - Multiplying matrices:Example: Find AB? ; Thank you for your attentionNatural Science Department

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