 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that, let A be equal to the matrix containing elements 1, 3, 2, 5 and B be equal to the matrix containing elements minus 11, 2. Find a matrix X such that AX is equal to B. Let P and Q be two matrices then the product PQ can be obtained if and only if number of columns in P is equal to number of rows in Q. With this key idea let us proceed with the solution. We are given A equal to the matrix containing elements 1, 3, 2, 5. Now as A is a 2 by 2 matrix therefore AX is possible if X is a matrix of order 2 by P where P is the number of columns so here as X is unknown therefore P is also unknown. Also if A is a matrix of order 2 by 2 and X is a matrix of order 2 by P therefore order of AX is equal to 2 by P. As we are given that AX is equal to B therefore order of AX is equal to order of B. This implies 2 by P is equal to 2 by 1. So P is equal to 1 hence we can see that X is of order 2 by 1. So let us suppose X is equal to matrix containing elements XY. As given in the question AX is equal to B this implies the matrix containing elements 1, 3, 2, 5 into the matrix containing elements XY is equal to the matrix containing elements minus 11, 2. On multiplying these two matrices we will obtain a matrix containing elements X plus 2 by 3X plus 5 by equal to matrix containing elements minus 11, 2. As we know if two matrices are equal their corresponding elements will be equal therefore we obtain the equations X plus 2 by is equal to minus 11 and 3X plus 5 by is equal to 2. This implies X is equal to minus 11 minus 2 by. Now putting the value of X in the equation 3X plus 5 by equal to 2 we get 3 into minus 11 minus 2 by plus 5 by is equal to 2 which implies minus 33 minus 6 by plus 5 by is equal to 2. This implies minus 33 minus Y is equal to 2 that is minus Y is equal to 2 plus 33 which is equal to 35. So Y is equal to minus 35. Now putting back the value of Y we have X is equal to minus 11 minus 2 into minus 35 which is equal to minus 11 plus 70 that is equal to 59. So X is equal to 59. As we had taken X equal to the matrix containing elements X and Y so X is equal to matrix containing elements 59 and minus 35 which is our answer. This completes our session. Hope you enjoyed this session.