 Hello and welcome to the session. In this session, we will discuss a question which says that for the given matrices and vectors, is the product defined? If yes, then find the product in the first part, this matrix and this vector that is the column vector is given to us and in the second part, this matrix and this column vector is given. And we will check whether these products are defined or not. If yes, then we have to find the product matrix. Now before starting the solution of this question, we should know a result. And that is, the product of two matrices A and B, that is A, B is defined when number of columns of matrix A is equal to number of rows of matrix B. Now this result, we work out as a key idea for solving the given question. Now let us start with the solution of the given question. Now in the first part, we have given a matrix and a vector. Now here, that is, dimension of this matrix is 3 is a column vector, that is, number of columns of the given matrix A and number of rows of the given vector. Number of columns of the given matrix A and B is defined when number of columns of matrix A is equal to number of rows of matrix B of the given matrix is not equal to number of rows of the given vector. It is not defined. We have given a matrix with elements in forward 1 and 2 in vector which is a matrix having single 1. Now here you can see this matrix number of this vector is also 3. Number of columns equal to number of rows of the given when the resulting matrix will be of order 2 cross 1. Now let us find the product and then we add the products of this vector and here we write 2 into 1 is 3 into minus 1 to obtain this product matrix of this matrix and this column of the given vector 1 plus 1 minus 1 plus 2 into 1. On simplifying, we have a matrix with element in first row and element in second row and minus 1 plus 2 matrix with element. So here we can see that the product of this matrix and vector again a column vector having elements given question. That is all for this session. Hope you all have enjoyed this session.