 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that find the matrix A of order 2 by 2 which satisfy the equation. The matrix containing elements 3, 2, 4, minus 1 into the matrix containing elements 1, 3, 0, 7 plus 3x is equal to the matrix containing elements 0, 2, 7, minus 1. First let us look at the LHS. We have to find the product of two matrices in the LHS that is the matrix containing elements 3, 2, 4, minus 1 into the matrix containing elements 1, 3, 0, 7. The product of these two matrices will be a 2 by 2 matrix in which the element in the first row first column is obtained by multiplying the first row of the first matrix by the first column of the second matrix that is 3 into 1 plus 4 into 3. The element in the first row second column is obtained by multiplying the first row of the first matrix by the second column of the second matrix that is 3 into 0 plus 4 into 7. Now the element in the second row first column is obtained by multiplying the second row of the first matrix by the first column of the second matrix that is 2 into 1 plus minus 1 into 3. Lastly the element in the second row second column is obtained by multiplying the second row of the first matrix with the second column of the second matrix that is 2 into 0 plus minus 1 into 7. This is equal to the matrix containing elements 3 plus 12, 2 minus 3, 0 plus 28 and 0 plus minus 7 which is equal to the matrix containing elements 15 minus 1, 28 and minus 7. So now the given matrix equation becomes the matrix containing elements 15 minus 1, 28 minus 7 plus 3x equal to the matrix containing elements 0, 2, 7 minus 1. This implies 3x will be equal to the matrix containing elements 0, 2, 7 minus 1 minus the matrix containing elements 15 minus 1, 28 and minus 7. For subtracting two matrices we have to subtract the corresponding elements of the matrix. So this is equal to matrix containing elements 0 minus 15, 2 minus minus 1, 7 minus 28 and minus 1 minus minus 7. This will be equal to the matrix containing elements minus 15, 2 plus 1, 7 minus 28 and minus 1 plus 7 which is equal to the matrix containing elements minus 15, 3 minus 21 and 6. So this implies x will be equal to 1 by 3 into the matrix containing elements minus 15, 3 minus 21, 6. We know that if we multiply a scalar by a matrix it has to be multiplied by every element of the matrix. So this will be equal to the matrix containing elements minus 15 by 3, 3 by 3 minus 21 by 3 and 6 by 3. So we have x is equal to the matrix containing elements minus 5, 1 minus 7 and 2 which is our answer. This completes our session. Hope you enjoyed the session.