 Hello and welcome to the session in this session we are going to discuss the following question and the question says that find p, q, r and s if the matrix containing elements to p plus q 5 r minus s p minus 2 q 4 r plus 3 s is equal to the matrix containing elements 4, 11 minus 3, 24. If two matrices are equal then both the matrices are of same order the corresponding elements are equal. With this key idea let us proceed with the solution. We are given that the matrix containing elements to p plus q 5 r minus s p minus 2 q 4 r plus 3 s is equal to the matrix containing elements 4, 11 minus 3, 24. As the two matrices are equal therefore the corresponding elements must also be equal. This implies that to p plus q is equal to 4 p minus 2 q is equal to minus 3 5 r minus s is equal to 11 and r plus 3 s is equal to 24. Let us mark these four equations as 1 2 3 take equation 1 that is to p plus q is equal to 4. This implies q is equal to 4 minus 2 p putting the value of q in equation 2 we have p minus 2 into 4 minus 2 p is equal to minus 3. This implies p minus 8 plus 4 p is equal to minus 3. This implies 5 p minus 8 is equal to minus 3. That is 5 p is equal to minus 3 plus 8 which is equal to 5. Therefore p is equal to 5 upon 5 which is equal to 1. So we have p is equal to 1. Put in back the value of p in equation 1 we have q is equal to 4 minus 2 into 1 which is equal to 4 minus 2 which is 2. So q is equal to 2. Now consider equation 3 that is 5 r minus s is equal to 11. This implies s is equal to 5 r minus 11 substituting the value of s in equation 4 that is in the equation 4 r plus 3 s is equal to 24 we get 4 r plus 3 into 5 r minus 11 is equal to 24. This implies 4 r plus 15 r minus 33 is equal to 24 which implies 19 r minus 33 is equal to 24. That is 19 r is equal to 24 plus 33 which is equal to 57 which implies r is equal to 57 upon 19 which is equal to 3. So we have r is equal to 3 putting back the value of s is equal to 5 r minus 11. We have s is equal to 5 into 3 minus 11 which is equal to 15 minus 11 that is 4. So s is equal to 4. Hence we obtain p equal to 1, q equal to 2, r is equal to 3 and s equal to 4 which is our answer. This completes our session. Hope you enjoyed this session.