BCA_Sem-1_Mathematics_Unit-1

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Unit 1: Matrix 2 All right are reserved with CU-IDOL • Introduction of a matrix • Its different kinds • matrix addition and scalar multiplication. www.cuidol.in Unit-1(MAP-607)

MATRIX Unit-1(MAP-607) 3 All right are reserved with CU-IDOL a matrix (plural matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. Matrices are commonly written in box brackets. The horizontal and vertical lines of entries in a matrix are called rows and columns, respectively. The size of a matrix is defined by the number of rows and columns that it contains. A matrix with m rows and n columns is called an m × n matrix or mm-by-nn matrix, while m and n are called its dimensions. www.cuidol.in

Matrix dimensions 4 The dimensions of a matrix tells its size: the number of rows and columns of the matrix, in that order. www.cuidol.in Unit-1(MAP-607) All right are reserved with CU-IDOL

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Row Matrix 7 A matrix having only one row is called a row matrix. Thus A = [aij]mxn is a row matrix if m = 1. So, a row matrix can be represented as A = [aij]1×n. It is called so because it has only one row and the order of a row matrix will hence be 1 × n. For example, A = [1 2 4 5] is row matrix of order 1 x 4. Another example of the row matrix is P = [ -4 -21 -17 ] which is of the order 1×3. Column Matrix A matrix having only one column is called a column matrix. Thus, A = [aij]mxn is a column matrix if n = 1. Thus, the value of for a column matrix will be 1. Hence, the order is m × 1. An example of a column matrix is: www.cuidol.in Unit-1(MAP-607) All right are reserved with CU-IDOL

8 Zero or Null Matrix www.cuidol.in Unit-1(MAP-607) All right are reserved with CU-IDOL

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17 Addition of Matrices If A[aij]mxn and B[bij]mxn are two matrices of the same order then their sum A + B is a matrix, and each element of that matrix is the sum of the corresponding elements. i.e. A + B = [aij + bij]mxn www.cuidol.in Unit-1(MAP-607) All right are reserved with CU-IDOL

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19 Subtraction of Matrices If A and B are two matrices of the same order, then we define A-B=A+(−B). www.cuidol.in Unit-1(MAP-607) All right are reserved with CU-IDOL

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21 Scalar Multiplication of Matrices www.cuidol.in Unit-1(MAP-607) All right are reserved with CU-IDOL

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REFERENCES 23 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

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