 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that if P is equal to the 2 by 2 matrix 5 minus 2 0 1, Q is equal to the 2 by 2 matrix 1 5 2 7, R is equal to the 2 by 2 matrix 4 7 10 5, then find 2P plus 3Q minus R. We have to find 2P plus 3Q minus R where P is equal to the 2 by 2 matrix 5 minus 2 0 1, Q is equal to the 2 by 2 matrix 1 5 2 7, R is equal to the 2 by 2 matrix 4 7 10 5. When we multiply a matrix by a scalar, it is multiplied by every element of the matrix. So 2P plus 3Q minus R is equal to 2 into the matrix 5 minus 2 0 1 plus 3 into the matrix 1 5 2 7 minus the matrix 4 7 10 5. Now by multiplying the scalars with every element of the matrix we get the matrix 5 into 2 0 into 2 minus 2 into 2 1 into 2 plus the matrix 1 into 3 2 into 3 5 into 3 and 7 into 3 minus the matrix 4 7 10 5. So this is equal to the matrix 10 minus 4 0 2 plus the matrix 3 15 6 21 minus the matrix 4 7 10 5. Now by matrix addition or subtraction for the first element in the matrix we add or subtract all the first elements that is 10 plus 3 minus 4. For the second element we add and subtract the second element of the three matrices that is 0 plus 6 minus 10 for the third element that is minus 4 plus 15 minus 7 and the fourth element will be 2 plus 21 minus 5 so here we get 10 plus 3 minus 4 is 9 6 minus 10 is minus 4 minus 4 plus 15 minus 7 is 4 and 2 plus 21 minus 5 is 18 therefore 2 p plus 3 q minus R is equal to the matrix 9 4 minus 4 18 which is our answer. This completes our session. Hope you enjoyed the session.