36 MATHEMATICS respectively Similarly in the second arrangement the entries in the first row represent the number of notebooks possessed by Radha Fauzia and Simran respectively The entries in the second row represent the number of pens possessed by Radha Fauzia and Simran respectively An arrangement or display of the above kind is called a matrix Formally we define matrix as Definition 1 A matrix is an ordered rectangular array of numbers or functions The numbers or functions are called the elements or the entries of the matrix We denote matrices by capital letters The following are some examples of matrices 2 5 A 0 5 3 6 B 3 5 3 2 i 3 Jou 1 7 5 N a 12 a22 m2 SUNNI In the above examples the horizontal lines of elements are said to constitute rows of the matrix and the vertical lines of elements are said to constitute columns of the matrix Thus A has 3 rows and 2 columns B has 3 rows and 3 columns while C has 2 rows and 3 columns 3 2 1 Order of a matrix A matrix having m rows and n columns is called a matrix of order m n or simply m n matrix read as an m by n matrix So referring to the above examples of matrices we have A as 3 x 2 matrix B as 3 x 3 matrix and C as 2 x 3 matrix We observe that A has 3 x 2 6 elements B and C have 9 and 6 elements respectively In general an m xn matrix has the following rectangular array C A 13 aj A23 x cosx sinx 2 or A almx 1 i m l j n i jEN n Thus the 7th row consists of the elements a consists of the elements a az azamj 1 x Rationalised 2023 24 am Azn in mn mxn a2 a3 ain while the 7th column In general a is an element lying in the 7th row and jth column We can also call it as the i j th element of A The number of elements in an m n matrix will be equal to mn MATRICES 37 Note In this chapter 1 We shall follow the notation namely A a to indicate that A is a matrix of order mx n