E-LESSON-8

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B.C.A 2 All right are reserved with CU-IDOL Mathematics Course Code: BCA114 Semester: First SLM UNITS : e-Lesson No.: 8 5 www.cuidol.in Unit-8 (BCA114)

Matrix 1 33 OBJECTIVES INTRODUCTION Student will be able to : In this unit we are going to learn about the Define Matrix. Matrix. Illustrate the Types of Matrix. Under this unit you will also understand the types of Matrix. Describe the Transpose Matrix. This Unit will also make us to understand the Transpose of a matrix. www.cuidol.in Unit-8 (BCA114) INASllTITriUgThEt aOrFeDreISsTeArNveCdE AwNitDh OCNUL-IIDNOE LLEARNING

TOPICS TO BE COVERED 4 • Definition of Matrix • Types of Matrix • Transpose of a Matrix www.cuidol.in Unit-8 (BCA114) All right are reserved with CU-IDOL

Matrix 5 Definition • A set of mn numbers (real or complex numbers) arranged in the form of a rectangular array having m rows and n columns is called on m × n matrix. • Different notations used for matrix are [ ], ( ) and ||. We are using notation [ ]. Example: [1 2 3]1x3 No. of columns 3 No. of rows 1 • Matrices with a single row are called row vectors, and those with a single column are called column vectors. A matrix with the same number of rows and columns is called a square matrix. • A matrix with an infinite number of rows or columns (or both) is called an infinite matrix. In some contexts, such as computer algebra programs, it is useful to consider a matrix with no rows or no columns, called an empty matrix. www.cuidol.in Unit-8 (BCA114) All right are reserved with CU-IDOL

Types of Matrix 6 •Row Matrix: A matrix containing one row and n number of columns is called Row Matrix. Example: [1 3 5] is row matrix of order 1x3. •Column Matrix: A matrix containing m number of rows and one column is called Column Matrix. www.cuidol.in Unit-8 (BCA114) All right are reserved with CU-IDOL

Types of Matrix 7 www.cuidol.in Unit-8 (BCA114) All right are reserved with CU-IDOL

Types of Matrix 8 www.cuidol.in Unit-8 (BCA114) All right are reserved with CU-IDOL

Types of Matrix 9 www.cuidol.in Unit-8 (BCA114) All right are reserved with CU-IDOL

Types of Matrix 10 www.cuidol.in Unit-8 (BCA114) All right are reserved with CU-IDOL

Types of Matrix 11 www.cuidol.in Unit-8 (BCA114) All right are reserved with CU-IDOL

Transpose of a Matrix 12 • Transpose of a Matrix: The matrix obtained from a given matrix, by interchanging its rows and columns, is called Transpose of a matrix. •If a matrix m × n contains m rows and n columns, then its transpose contains n rows and m columns. If the given matrix is A, then its transpose is denoted by A’. www.cuidol.in Unit-8 (BCA114) All right are reserved with CU-IDOL

MULTIPLE CHOICE QUESTIONS 1) A symmetric matrix is a one in which 13 a) All diagonal elements are zero c) A = A^T b) All diagonal elements are 1 d) A = -A^T 2) A matrix having one row and many columns is known as? d) None of the mentioned a) Row matrix b) Column matrix c) Diagonal matrix 3) A matrix having many rows and one column is known as? d) None of the mentioned a) Row matrix b) Column matrix c) Diagonal matrix 4) A square matrix A = [aij]nxn, if aij = 0 for i < j then that matrix is known as: d) Null matrix a) Upper triangular matrix b) Lower triangular matrix c) Unit matrix 5) If A is a matrix of order m × n, then it contains (a) n rows (b) m rows (c) m × n rows (d) None of these Answers: 1) c) 2.a) 3.b) 4.b) 5.b) www.cuidol.in Unit-8 (BCA114) All right are reserved with CU-IDOL

SUMMARY 14 Let us recapitulate the important concepts discussed in this session: •A set of mn numbers (real or complex numbers) arranged in the form of a rectangular array having m rows and n columns is called on m × n matrix. •Row Matrix: A matrix containing one row and n number of columns is called Row Matrix. •Column Matrix: A matrix containing m number of rows and one column is called Column Matrix. •A square matrix each of whose diagonal elements are 1 and non-diagonal elements are 0 are called unit matrix. Denoted by “Im×n”. • A matrix whose number of rows is equal to number of columns, i.e., m = n is called square matrix. • A diagonal matrix whose all diagonal elements are equal is called scalar matrix. • The matrix obtained from a given matrix, by interchanging its and columns, is called Transpose of a matrix. If a matrix m × n contains m rows and n columns, then its transpose contains n rows and m columns. www.cuidol.in Unit-8 (BCA114) All right are reserved with CU-IDOL

FREQUENTLY ASKED QUESTION 15 Q1: Define Matrix. Ans: A set of mn numbers (real or complex numbers) arranged in the form of a rectangular array having m rows and n columns is called on m × n matrix. For more details refer subject SLM unit 8. Q2: Explain identity Matrix. Ans: A square matrix each of whose diagonal elements are 1 and non-diagonal elements are 0 are called unit matrix. Denoted by “Im×n”. For more details refer subject SLM unit 8. Q3. Explain Transpose Matrix. Ans. The matrix obtained from a given matrix, by interchanging its and columns, is called Transpose of a matrix. If a matrix m × n contains m rows and n columns, then its transpose contains n rows and m columns. For more details refer subject SLM unit 8. www.cuidol.in Unit-8 (BCA114) All right are reserved with CU-IDOL

REFERENCES 16 CU-IDOL’s “Mathematics” SLM. Seymour Lipschutz, Marc Lars Lipson, “Discrete Mathematics”, Publisher: McGraw Hill Education (India) Private Limited.  J.K. Sharma, “Discrete Mathematics”, Publisher: MacMillan India Limited. K. Chandrasekhara Rao, “Discrete Mathematics”, Publisher: Narosa Publishing House. Dr. Abhilasha S. Magar, “Applied Mathematics – I”, Publisher: Himalaya Publishing House. Dr. B.S. Grewal, “Higher Engineering Mathematics”, Publisher: Khanna Publishers, Delhi. 8. Mr. K.A. Stroud, “Engineering Mathematics”, Publisher: The MacMillan Press Ltd., London, Basingstoke. www.cuidol.in Unit-8 (BCA114) All right are reserved with CU-IDOL

17 THANK YOU For queries Email: [email protected] www.cuidol.in Unit-8 (BCA114) All right are reserved with CU-IDOL