 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that solve minus 3 into 2 by 2 matrix containing elements 2x y 2 plus z 2w plus 1 by 3 is equal to 2 by 2 matrix containing elements 6 minus 27, 12, 14 for x, y, z and w. Now let us start with the solution of this question. We have to solve the equation that is minus 3 into 2 by 2 matrix containing elements 2x y 2 plus z 2w plus 1 by 3 is equal to 2 by 2 matrix containing elements 6 minus 27. We see that there is equality of 2 matrices and we see that in the left hand side scalar minus 3 is multiplied by this matrix. So first we will simplify it. Here the scalar will be multiplied by each element in the matrix and this is equal to a 2 by 2 matrix containing elements minus 3 into 2x minus 3 into y minus 3 into 2 plus z the whole and minus 3 into 2w plus 1 by 3 the whole and this is equal to a 2 by 2 matrix containing elements minus 3 into 2x that is minus of 6x minus 3 into y that is minus 3y. Now minus 3 into 2 will be minus 6 then minus 3 into z will be minus of 3z. Now minus 3 into 2w will be equal to minus of 6w then minus 3 into 1 by 3 will be equal to minus of 1. Therefore we have got minus 3 into 2 by 2 matrix containing elements 2x y 2 plus z 2w plus 1 by 3 as 2 by 2 matrix containing elements minus of 6x minus of 3y minus 6 minus 3z minus 6w minus 1. And therefore we get 2 by 2 matrix containing elements minus 6x minus 3y minus 6 minus 3z minus 6w minus 1 is equal to 2 by 2 matrix containing elements 6 minus 27 12 14. Now we know that 2 matrices are equal if their corresponding elements are equal. So we equate the corresponding elements in the 2 matrices and we get the following equations that is minus of 6x is equal to 6 and minus of 3y is equal to minus of 27 minus of 6 minus 3z is equal to minus of 6 minus 3z. Now we get minus 6 is equal to 12 and minus of 6w minus 1 is equal to 14. Now we solve these equations one by one and first we have minus 6x is equal to 6. Now dividing by minus 6 on both sides we get x is equal to minus 1 so value of x is minus 1. Now we take second equation that is minus of 3y is equal to minus of 27. Now dividing by minus 3 on both sides we get y is equal to 9 so value of y is equal to 9. Now next equation is minus of 6 minus of 3z is equal to 12 which implies that minus of 3z is equal to 12 plus 6 which further implies minus of 3z is equal to 18. Now dividing both the sides by minus 3 we get z is equal to minus 6 so the value of z is equal to minus 6. And the last equation is minus of 6w minus 1 is equal to 14 which implies that minus of 6w is equal to 14 plus 1 that is minus of 6w is equal to 15. Now dividing both sides by minus 6 we get w is equal to minus of 15 by 6 which is equal to 3 into 2 is 6 and 3 into minus 5 is minus 15. So value of w will be equal to minus of 5 by 2 so we have x is equal to minus 1, y is equal to 9, z is equal to minus 6 and w is equal to minus 5 by 2 which is the required answer. This completes our session. Hope you enjoyed this session.