1. 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: 20082009201020112012 I300420360450600 II310250300210340 III600630670610700

2. 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

3. 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.

4. Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department 300420360450600 310250300210340 600630670610700

5. Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department 300420360450600 310250300210340 600630670610700

6. 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.

7. Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department 300420360450600 310250300210340 600630670610700

8. 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.

9. Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department Example:

10. Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department

11. 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

12. Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department

13. Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department

14. 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.

15. Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department

16. Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department

17. 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

18. 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.

19. 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?

20. 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.

21. 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?

22. 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?

23. 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:

24. 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?

25. Company LOGO Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix Natural Science Department ;