BCA_Sem-1_Mathematics_Unit-2

IDOL Institute of Distance and Online Learning ENHANCE YOUR QUALIFICATION, ADVANCE YOUR CAREER.

2 Unit 1: Matrix • Multiplication of matrices • Square matrix. www.cuidol.in Unit-1(MAP-607) All right are reserved with CU-IDOL

Matrix Multiplication 3 Row by Column Multiplication The product of matrix A and B is found by multiplying the rowof matrix A by the columnof matrix B. addingThen the final products www.cuidol.in Unit-1(MAP-607) All right are reserved with CU-IDOL

4 www.cuidol.in Unit-1(MAP-607) All right are reserved with CU-IDOL

5 www.cuidol.in Unit-1(MAP-607) All right are reserved with CU-IDOL

Exercise 6 Examples: 1) Given the dimensions of the following matrices determine if they can be multiplied if so find the dimensions of their product: A is a 3 x 5 B is a 2 x 5 C is a 5 x 1 D is a 3 x 2 www.cuidol.in Unit-1(MAP-607) All right are reserved with CU-IDOL

7 www.cuidol.in Unit-1(MAP-607) All right are reserved with CU-IDOL

8 Find the product of the given matrices: www.cuidol.in Unit-1(MAP-607) All right are reserved with CU-IDOL

9 Find the product of the given matrices www.cuidol.in Unit-1(MAP-607) All right are reserved with CU-IDOL

What is a Square 10 Matrix? A square matrix is a special type of matrix in which the number of rows is equal to the number of columns. If a square matrix has n rows and n columns, it is said to be of the order n. As the name suggests, the matrix looks like a square. Square matrices can be of the order 1, 2, or any number, n. www.cuidol.in Unit-1(MAP-607) All right are reserved with CU-IDOL

11 www.cuidol.in Unit-1(MAP-607) All right are reserved with CU-IDOL

•Identity Matrix 12 All right are reserved with CU-IDOL •This is a special type of square matrix where the values of a square matrix, other than its diagonal, are zeros. Below we show identity matrices of order 1, 2, and 3. www.cuidol.in Unit-1(MAP-607)

How to Square a Matrix 13 Square Matrix is a type of matrix. But when we are talking about squaring a matrix, we are actually doing an operation of multiplying a matrix by itself. So, how do we square a matrix? If we were to square a Matrix A, we would multiply Matrix A by itself. It will follow the process of matrix multiplication. We show the squaring of a 2×2 matrix below www.cuidol.in Unit-1(MAP-607) All right are reserved with CU-IDOL

How to Square a Matrix 14 www.cuidol.in Unit-1(MAP-607) All right are reserved with CU-IDOL

Exercise 15 www.cuidol.in Unit-1(MAP-607) All right are reserved with CU-IDOL

16 www.cuidol.in Unit-1(MAP-607) All right are reserved with CU-IDOL

17 EXERCISE www.cuidol.in Unit-1(MAP-607) All right are reserved with CU-IDOL

CHECK A.B=B.A 18 www.cuidol.in Unit-1(MAP-607) All right are reserved with CU-IDOL

REFERENCES 19 TEXTBOOKS T1 Veerarajan, T. “Discrete Mathematics”, Tata-McGrawHill, New Delhi. T2 Singaravelu, A. “Allied Mathematics”, Meenakshi Agency, Chennai. REFERENCE BOOKS R1Vittal, P.R, “Allied Mathematics”, Reprint,Margham Publications, Chennai. R2 Venkata chalapathy, S.G, “Allied Mathematics”, Margham Publications, Chennai. www.cuidol.in Unit-1(MAP-607) All right are reserved with CU-IDOL

20 THANK YOU www.cuidol.in Unit-1(MAP-607) All right are reserved with CU-IDOL