 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that if P minus Q is equal to the 2 by 2 matrix 5029 and P plus Q is the 2 by 2 matrix 306 minus 1, find the matrices P and Q. We are given P minus Q is equal to the matrix 5029, mark this equation as 1 and P plus Q is equal to 306 minus 1, mark this as equation 2. Now let us add equation 1 and equation 2. So we get P minus Q plus P plus Q is equal to the matrix 5029 plus 306 minus 1. For addition of 2 matrices we have to add their corresponding elements. So we have 2P is equal to the matrix 5 plus 3, 2 plus 6, 0 plus 0, 9 minus 1 which is equal to 5 plus 3 is 8, 0, 6 plus 2 is 8, 9 minus 1 is 8. This implies P is equal to 1 by 2 of the matrix 8088. Again when a matrix is multiplied by a scalar, the scalar has to be multiplied by every element of the matrix. So we get the matrix 8 by 2, 8 by 2, 0, 8 by 2 which is equal to 4044. Now substituting the value of P equal to the matrix 4044 in equation 2 that is P plus Q equal to 306 minus 1, we have 4044 that is P plus Q is equal to 306 minus 1. This implies Q is equal to 306 minus 1 minus 4044. So now as for subtraction of 2 matrices, we have to subtract the corresponding elements of the matrices. We get Q is equal to the matrix 3 minus 4, 6 minus 4, 0 minus 0, minus 1, minus 4. This implies that Q is equal to minus 1, 0, 2, minus 5. So finally we have P is a 2 by 2 square matrix 4044 and Q is also a 2 by 2 square matrix minus 1, 0, 2, minus 5 which is our answer. This completes our session. Hope you enjoyed the session.