 Hello and welcome to the session. In this session we will use mattresses to represent and manipulate data. Now suppose you are going to have it to buy milk, butter and bread. Now you visit 2 stores and B. Now in store A, bread cost 2 dollars, milk cost 1.50 dollars, butter cost side dollars and in store B the cost of bread, milk and butter is 2.50 dollars, 1.60 dollars and 2.20 dollars respectively. Now we want to arrange this data in row and column form. One method we already know is two-way tables. Now let us consider the following two-way table Suppose the cost in dollars of bread, butter and milk in stores that is store A and store B. Now matrix is a terminal array of numbers arranged in rows and now this table has, now this is, this is row 2, this is row 3, this is column and this is in a matrix. So this will be the cost matrix, the prices in rows and columns within a square bracket. So this represents this row 2 to products matrix with elements 2.50, elements in second row as 1.50, 1.6935 is called an element of the matrix. Now let us discuss dimension of a matrix, number of rows and columns gives dimension. Now the above matrix or dimension in a matrix of order m plus n will be the product, the order of the given matrix. It means number of elements. Now let us discuss representation of matrix. Now we generally denote a matrix by in capital letter C with elements in first row as 0.50, elements in second row as 1.50, 1.60 and elements of matrix are generally denoted by ij and j is jth column. j means element in ith row and jth column. Now suppose equal to 3 and j is equal to 2. It means we have to find element in third row and second column. Now here this is the third row element and second column is equal to 2.20 that is element in second row and that element is 1.50. So this is the general of a matrix and c matrix. Now at the c matrix the connection between the rows and columns elements are mostly denoted by, now let us discuss an example. The classmates are asked to indicate with whom they would like to go into a movie. The response is summarized in a matrix. The matrix is read from row to column. 1 means yes and 0 means the matrix will like to go with which column members and whether c would like to go with d or not c. To capital letter c the element corresponding to d in that row means yes to movie c from the matrix that a will like to go to movie with b like to go alone and d. So in this way you can read this matrix. And now let us discuss network and matrices of which are connected with the points or vertices out in a line. Now let us see the two. One has arrows on the lines which tell us which we can move from one row to other. The lines are called only in one direction along the line. Then draw here of nodes that are directly connected by a matrix can be used to store information about networks. This is also called adjacency matrices. Now let us see the following network between the houses of and d. These parts can be displayed when dimension of matrix that is number of rows is equal to number of columns that we have from one vertex to the other. And we read the matrix from row to column and this is a directed network. Only in given direction from d to we cannot move. Then in rows we write we write nodes b c. Now in the first row that is from node a to node a in this network. Entry is 0. Then second and in this network from a to b from a to c there is one path we can move from d to a but we cannot there is no path. That means 0 we write elements and we get we have discussed the data in matrix form and this completes our session hope you all have enjoyed the session. Thank you.