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**Example 1:**The following rectangular array describes the profit (milions dollar) of 3 branches in 5 years:**DuyTân University**Natural Science Department Module 1: MATRIX Lecturer: Thân Thị Quỳnh Dao 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.**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.**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.**2. Some special matrices**- Row-matrix:A matrix with only 1 row. A general row matrix would be written as or - Column-matrix: A matrix with only 1column. A general column matrix would be written as or**2. Some special matrices**- Square matrix of order n: A matrix with n rows, n columns. A general square matrix of order nwould 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?**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? Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix**Natural Science Department**Thank you for your attention ;