MATRICES MATRICES of notebooks and pens by Radha and her two friends Fauzia and Simran which is as follows: Radha has notebooks pens, Fauzia has notebooks pens, Simran has notebooks pens. Now this could be arranged in the tabular form as follows: Notebooks Pens Radha Fauzia Simran and this can be expressed as Radha Fauzia Simran Notebooks Pens which can be expressed as: In the first arrangement the entries in the first column represent the number of note books possessed by Radha, Fauzia and Simran, respectively and the entries in the second column represent the number of pens possessed by Radha, Fauzia and Simran, 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 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: – , . – i , C tan 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 rows and columns, B has rows and columns while C has rows and columns. .
. 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 × matrix, B as × matrix and C as × matrix. We observe that A has × = elements, B and C have and elements, respectively.
In general, an m × n matrix has the following rectangular array: A = [ a ij ] m × n , ≤ i ≤ m , ≤ j ≤ n i , j ∈ N Thus the i th row consists of the elements a i , a i , a i ,..., a in , while the j th column consists of the elements a j , a j , a j ,..., a mj , In general a ij , is an element lying in the i th row and j th 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