Module 1: Matrix

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.
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Module 1: Matrix NaturalScienceDepartmentCompanyLOGO 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 Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix DuyTânUniversity NaturalScienceDepartment Module 1: MATRIX Lecturer: Thân CompanyThị Quỳnh Dao LOGOChapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix NaturalScienceDepartment Company LOGO 1. Definition- A matrix is a rectangular array of numbers. The numbers inthe array are called the entries in the matrix. Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix NaturalScienceDepartmentCompanyLOGO 300 420 360 450 600 310 250 300 210 340 600 630 670 610 700 Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix NaturalScienceDepartmentCompanyLOGO 300 420 360 450 600A3 5 = 310 250 300 210 340 600 630 670 610 700 Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix NaturalScienceDepartment Company LOGO 1. Definition- A matrix is a rectangular array of numbers. The numbers inthe 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 rowsand columns it contains. Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix NaturalScienceDepartmentCompanyLOGO a11 = 300 300 420 360 450 600A3 5 = 310 250 300 210 340 600 630 670 610 700 a24 = 210 Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix NaturalScienceDepartment Company LOGO 1. Definition- Let m,n are positive integers. A general mxn matrix is arectangular array of number with m rows and n columns as � a11 a12 a13 ... a1j ... a1n � � a 21 a 22 a 23 ... a 2j ... a 2n � � � �... ... ... ... ... ... ... �A m×n =� �= � a � �a i1 a i2 a i3 ... a ij ... a in � � � ij m×n �... ... ... ... ... ... ... � � � � a m1 a m2 a m3 ... a mj ... a mn � a ij : the entry occurs in row i and column j. Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix NaturalScienceDepartmentCompanyLOGO Example: 1 �� �� 6 A = [ 100] B= �� C = [ 0 −3 100] �� 7 �� 0 �� 1 � 2 3 4� � 2 3 4 5� −5 4 −9 2 0 � � D= � � E=� � � 3 4 5 6� �4 3 7 8 2 � � � 4 � 5 6 7� Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix NaturalScienceDepartmentCompanyLOGO A = [ 3 5] B = [ 7 9 2 4] C = [ 2 5 7 8 2 3 0] Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix NaturalScienceDepartment Company LOGO 2. Some special matrices- Row-matrix: A matrix with only 1 row. A general row matrixwould be written as A1 n = [ a11 a12 a13 ... a1n ] � aij � . or � � 1 n- Column-matrix: A matrix with only 1 column. A generalcolumn matrix would be written as �a11 � �a � Am 1 = � 21 � � aij � . �... � or � � m 1 � � �am1 � Chapter 1: Matrix, Determinant, System of linear equations Module 1: Matrix ...