 Hello and welcome to the session. In this session, we are going to discuss the following question and the question states that, find the matrix X such that a plus 2x is equal to 3b where a is the matrix 1 minus 2, 4, 3 and b is the matrix 3, 0, 2, minus 3. We need to find the matrix X in the equation a plus 2x is equal to 3b where a is the matrix 1 minus 2, 4, 3 and b is the matrix 3, 0, 2, minus 3 as we can see that a and b are both 2 by 2 matrices. Therefore, the matrix that we will obtain for X will also be a 2 by 2 matrix. Now, as b is equal to the matrix 3, 0, 2, minus 3, therefore 3b will be equal to 3 into the matrix 3, 0, 2, minus 3. When a matrix is multiplied by a scalar, the scalar has to be multiplied by every element of the matrix. So, 3b is equal to the matrix 3 into 3, 2 into 3, 0 into 3, minus 3 into 3 which is equal to 9, 6, 0, minus 9. Now, as a plus 2x is equal to 3b, therefore 2x is equal to 3b minus a. As 3b is equal to the matrix 9, 0, 6, minus 9, so we have 2x is equal to the matrix 9, 0, 6, minus 9, minus a that is 1, minus 2, 4, 3. Now, when we subtract 2 matrices, then we have to subtract the corresponding elements of the 2 matrices, therefore we have the matrix 9, minus 1, 6, minus 4, 0, minus, minus 2, minus 9, minus 3. So, this is equal to the matrix 8, 2, 2, minus 12. Therefore, we have 2x is equal to the matrix 8, 2, 2, minus 12. This implies x is equal to 1 by 2 into the matrix 8, 2, 2, minus 12. Again, as we know when a matrix is multiplied by a scalar, then this scalar has to be multiplied by every element of the matrix. So, we get this is equal to the matrix 8 by 2, 2 by 2, 2 by 2 and minus 12 by 2. Therefore, the matrix x is equal to 4, 1, 1, minus 6. Hence, this is our answer. This completes our session. Hope you enjoyed this session.