E-LESSON-9

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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.: 9 6 www.cuidol.in Unit-9 (BCA114)

Matrix 2 33 OBJECTIVES INTRODUCTION Student will be able to : In this unit we are going to learn about the Explain Addition of Matrix. Matrix operations. Illustrate the Subtraction of Matrix. Under this unit you will understand the addition and subtraction. Describe the Multiplication of two Matrix. This Unit will also make us to understand the Scalar Multiplication of matrix. www.cuidol.in Unit-9 (BCA114) INASllTITriUgThEt aOrFeDreISsTeArNveCdE AwNitDh OCNUL-IIDNOE LLEARNING

TOPICS TO BE COVERED 4 • Matrix •Equal Matrices •Addition of Matrix •Subtraction of Matrix •Multiplication of Scalar Matrix •Multiplication of Two Matrices www.cuidol.in Unit-9 (BCA114) All right are reserved with CU-IDOL

Matrix 5 Introduction 1. A matrix is arrangement of mn numbers in m rows and n columns, written in rectangular or round bracket. 2. Rows are sleeping lines. 3. Columns are standing lines. 4. In simple terms, a matrix can be written as A = [aij]m×n 5. www.cuidol.in Unit-9 (BCA114) All right are reserved with CU-IDOL

Equal Matrices 6 •Two matrices are equal if they have the same dimension or order and the corresponding elements are identical. www.cuidol.in Unit-9 (BCA114) All right are reserved with CU-IDOL

Addition of Matrix 7 •In mathematics, matrix addition is the operation of adding two matrices by adding the corresponding entries together. However, there are other operations which could also be considered as a kind of addition for matrices, the direct sum and the Kronecker sum. •If A = [aij] and B = [bij] are two matrix of the same order, m × n, then the sum of the two matrices A and B is another matrix C = [cij] of the same order m × n, where cij = aij + bij. • If A = (aij)m, n and B = (bij)m, n then their sum A + B is the matrix C = (cij)m,n where cij = aij + bij, i = 1, 2, 3, ...... , m, j = 1, 2, 3, ...., n. www.cuidol.in Unit-9 (BCA114) All right are reserved with CU-IDOL

Subtraction of Matrix 8 •If A = [aij] and B = [bij] are two matrices of the same order, m × n, then the subtraction of the two matrices A and B is another matrix C = [cij] of the same order m × n, where, cij = aij – bij. www.cuidol.in Unit-9 (BCA114) All right are reserved with CU-IDOL

Multiplication of Scalar Matrix 9 •If a matrix A = [aij] of order m × n is to be multiplied by a scalar k, where k is not = 0, then the scalar multiplication KA of the matrix A is obtained by multiplying every element of A by scalar constant K. Hence, KA = [kaij]. Example: www.cuidol.in Unit-9 (BCA114) All right are reserved with CU-IDOL

Multiplication of Two Matrices 10 •In order to multiply two matrices, we have to learn the method of multiplying a row by a column first. If A is a row matrix and B is column matrix, A × B can be found provided the number of column of A = the number of rows of B. •Hence, if the order of A is 1 × m and the order of B is m × 1, only then we can find AB and the order of AB is 1 × 1. www.cuidol.in Unit-9 (BCA114) All right are reserved with CU-IDOL

MULTIPLE CHOICE QUESTIONS 11 1) Let A and B be two matrices of same order ,then state whether the given statement is true or false: A+B=B+A a) True b) False 2) Let A=[aij ] be an mxn matrix and k be a scalar then kA is equal to : a) [kaij ]mxn b) [aij/k ]mxn c) [k2 aij ]mxn d) None of the mentioned 3) For matrix A, B if A – B = O, where O is a null matrix then a) A = O b) B = O c) A = B d) None of the mentioned 4) If for a square matrix A and B,null matrix O, AB =O implies BA=O: a) True b) False 5) The order of matrix is never ____________. (a) Zero (b) One (c) Three (d) None of the above Answers: 1)a) 2) a) 3) c) 4) b) 5) a) www.cuidol.in Unit-9 (BCA114) All right are reserved with CU-IDOL

SUMMARY 12 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. •Equal Matrix: Two matrices are equal if they have the same dimension or order and the corresponding elements are identical. •If A = [aij] and B = [bij] are two matrix of the same order, m × n, then the sum of the two matrices A and B is another matrix C = [cij] of the same order m × n, where cij = aij + bij. •If a matrix A = [aij] of order m × n is to be multiplied by a scalar k, where k is not = 0, then the scalar multiplication KA of the matrix A is obtained by multiplying every element of A by scalar constant K. Hence, KA = [kaij]. www.cuidol.in Unit-9 (BCA114) All right are reserved with CU-IDOL

FREQUENTLY ASKED QUESTION 13 Q:1 Explain addition of two Matrix. Ans: If A = (aij)m, n and B = (bij)m, n then their sum A + B is the matrix C = (cij)m,n where cij = aij + bij, i = 1, 2, 3, ...... , m, j = 1, 2, 3, ...., n. For more details refer subject SLM unit 9. Q2: Explain Subtraction of two Matrix. Ans: If A = [aij] and B = [bij] are two matrices of the same order, m × n, then the subtraction of the two matrices A and B is another matrix C = [cij] of the same order m × n, where, cij = aij – bij. For more details refer subject SLM unit 9. Q3. Explain multiplication of two Matrix. Ans. In order to multiply two matrices, we have to learn the method of multiplying a row by a column first. If A is a row matrix and B is column matrix, A × B can be found provided the number of column of A = the number of rows of B. For more details refer subject SLM unit 9. www.cuidol.in Unit-9 (BCA114) All right are reserved with CU-IDOL

REFERENCES 14 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-9 (BCA114) All right are reserved with CU-IDOL

15 THANK YOU For queries Email: [email protected] www.cuidol.in Unit-9 (BCA114) All right are reserved with CU-IDOL