 Hi and welcome to the session I am Shashi and I am going to help you with the following question. The question is using elementary transformations, find the inverse of each of the matrices if it exists. Given matrices 2, 1, 4, 2. Let us start the solution now. Let A is equal to matrix 2, 1, 4, 2. Now to find inverse by row transformation method we will write A is equal to I A or we can write matrix 2, 1, 4, 2 is equal to matrix 1, 0, 0, 1 multiplied by A. Now we will apply sequence of row operations simultaneously on matrix A on left hand side and the matrix I on the right hand side. We will perform the matrix operations till we obtain identity matrix on the left hand side. Now we know the identity matrix has all the diagonal elements equal to 1. So to make this element equal to 1 we will apply on R1 row operation 1 upon 2 R1. So applying R1 row operation 1 upon 2 R1 we get 1 upon 2, 4, 2 matrix is equal to matrix 1 upon 2, 0, 0, 1 multiplied by A. Now to make this element equal to 0 we will apply on R2 row operation R2 minus 4 R1. So we can write applying row operation R2 minus 4 R1 we get matrix 1 upon 2, 0, 0 is equal to matrix 1 upon 2, 0, minus 2, 1 multiplied by A. Now the left side matrix have all zeros in the second row so it is impossible to convert it into identity matrix. Therefore inverse of the given matrix does not exist. So we can write same second row of the matrix on left hand side have all zeros so the inverse of A does not exist. So our final answer is inverse the given matrix does not exist. So this is our final answer this completes the session hope you enjoyed the session good bye.