 Hi, and welcome to the session. I am Shashi. Let us do one question. Question is, find a transpose of each of the following matrices. First matrix is 5, 1 upon 2 minus 1. Second matrix is 1, minus 1, 2, 3. Third matrix is minus 1, 5, 6, root 3, 5, 6, 2, 3, minus 1. First of all, let us understand the key idea to solve the given question. If A is equal to matrix A ij of order m into n, then the matrix obtained by interchanging the rows and columns of A is called transpose of A. Transpose of A is denoted by A dash. In other words, if A is equal to matrix A ij of the order m into n, then A transpose is equal to matrix A ji of the order n into n. Let us start with the solution part given to us as matrix 5, 1 upon 2, minus 1. Now clearly we can see this matrix has 3 rows and 1 column. That is, it is of the order 3 into 1. So, we can write transpose of matrix 5, 1 upon 2, minus 1 is matrix 5, 1 upon 2, minus 1. We can see this matrix is of order 1 into 3. We have changed this column into row or we can say the 3 rows have been changed into 3 columns or one column has been changed into one row in the transpose of the given matrix. The required matrix for the first part is 5, 1 upon 2, minus 1 matrix. Now second matrix given to us is 1, minus 1, 2, 3. We have to find the transpose of this matrix. So, we can write transpose of matrix 1, minus 1, 2, 3 is, we can see first row of the given matrix will change into first column of the transpose matrix and second row of the given matrix will change into second column of the transpose matrix. We can see first column of given matrix has changed into first row of the transpose matrix and the second column of the given matrix has changed into second row of the transpose matrix. From key idea, we know that transpose of a matrix is obtained by interchanging the rows and columns. So, that is what we have done here. So, transpose of 1, minus 1, 2, 3 matrix is matrix 1, 2, minus 1, 3. Now the third part given to us is matrix minus 1, 5, 6, root 3, 5, 6, 2, 3, minus 1. This matrix is of the order 3 into 3, that is it is having 3 rows and 3 columns. So, transpose of the given matrix is matrix, you know first row of the given matrix that is minus 1, 5, 6 will change into first column of the transpose matrix. Second row of the given matrix will change into second column of the transpose matrix and third row of the given matrix will change into third column of the transpose matrix. So, the transpose of the given matrix is minus 1, root 3, 2, 5, 5, 3, 6, 6, minus 1. It is the required answer for the first part is matrix 5, 1 upon 2, minus 1. It is required answer for second part is matrix 1, 2, minus 1, 3, required matrix. For third part is minus 1, root 3, 2, 5, 5, 3. This completes the session. Hope you understood the session. Have a nice day.