 Hi and welcome to the session. I am Shashi. Let us do one question. Question is, if A is equal to matrix minus 1, 2, 3, 5, 7, 9, minus 2, 1, 1 and B is equal to matrix minus 4, 1, minus 5, 1, 2, 0, 1, 3, 1. Then verify that A plus B whole transpose is equal to A transpose plus B transpose. First of all, let us understand the key idea to solve the given question. If A is equal to matrix Aij of the order m into n, then the matrix obtained by interchanging the rows and columns of A is called transpose of A. Transpose of matrix A is denoted by A dash. In other words, if A is equal to matrix Aij of the order m into n, then A transpose that is A dash is equal to matrix Aji of the order n into m. Let us now start with the solution. We are given A is equal to matrix minus 1, 2, 3, 5, 7, 9, minus 2, 1, 1 and B is equal to matrix minus 4, 1, minus 5, 1, 2, 1. Now, let us first of all find out A plus B. We know A plus A would be equal to matrix A plus matrix B. So, we can write minus 1, 2, 3, 5, 7, 9, minus 2, 1, 1 plus minus 4. 1 minus 5, 1, 2, 0 and 1, 3, 1. Now, this would be equal to matrix minus 1 plus minus 4, 2 plus 1, 3 plus minus 5. We can see minus 1 plus minus 4, 2 plus 1, 3 plus minus 5. We are adding the corresponding elevates of the two matrices. 5 plus 1, now 7 plus 2, then 9 plus 0, now minus 2 plus 1, 1 plus 3, 1 plus 1. A plus B matrix is equal to minus 5, 3, minus 2, 6, 9, 9, minus 1, 4, 2. Now we will find A plus B transpose. We know transpose of a matrix is obtained by interchanging the rows and columns as we have already read in key idea. So, first row minus 5, 3, minus 2 of the matrix A plus B will become the first column of matrix A plus B dash. So, we write minus 5, 3, minus 2 as the first column of A plus B transpose. Now, second row 6, 9, 9 will become second column of the transpose matrix of A plus B. So, we will write 6, 9, 9 as the second column of A plus B transpose. Now, third row minus 1, 4, 2 will become the third column of A plus B transpose. Write minus 1, 4, 2 as the third column of A plus B transpose. So, we get A plus B transpose equal to minus 5, 6, minus 1, 3, 9, 4, minus 2, 9, 2. Now, A plus B transpose is the left hand side of the expression that we have to verify. So, now we will find out the right hand side of the expression that is A transpose plus B transpose. We know A given in the question is minus 1, 2, 3, 5, 7, 9, minus 2, 1, 1 matrix. So, we can find out A transpose that would be equal to first row will change into first column of A transpose. Write second row of matrix A will change into second column of A transpose. Then third row of matrix A will change into third column of A transpose. So, we get A transpose equal to minus 1, 5, minus 2, 2, 7, 1, 3, 9, 1 matrix. Now, let us find out B transpose. The matrix B that is given in the question is equal to minus 4, 1, minus 5, 1, 2, 0, 1, 3, 1. Now, we will find B transpose. B transpose is equal to first row of matrix B will change into first column of B transpose. So, we get minus 4, 1, minus 5 as first column of B transpose. Second row of matrix B will change into second column of B transpose. So, we write 1, 2, 0 as second column of B transpose. Now, third row of matrix B will change into third column of B transpose. So, we get B transpose is equal to matrix minus 4, 1, 1, 1, 2, 3, minus 5, 0, 1. Now, we will find A transpose plus B transpose that is the right hand side of the expression that we have to verify in the question. So, we will substitute the value of A transpose that is matrix A transpose in place of A dash. So, we get minus 1, 5, minus 2, 2, 7, 1, 3, 9, 1 matrix as A transpose. Now, we will write B transpose here that is the matrix minus 4, 1, 1, 1, 2, 3, minus 5, 0, 1. Now, this is equal to we will add corresponding elements of the two matrices. So, we will get minus 1 plus minus 4, 5, plus 1, minus 2, plus 1, 2, plus 1, 7, plus 2, 1, plus 3, 3, plus minus 5, 9, plus 0, 1, plus 1. This implies A transpose plus B transpose is equal to matrix. We know minus 1 plus minus 4 is equal to minus 5, 5 plus 1 is equal to 6, minus 2 plus 1 is minus 1, 2 plus 1 is 3, 7 plus 2 is 9, 1 plus 3 is 4, 3 plus minus 5 is minus 2, 9 plus 0 is 9, 1 plus 1 is equal to 2. So, A transpose plus B transpose is equal to matrix minus 5, 6, minus 1, 3, 9, 4, minus 2, 9, 2. But this matrix is same as matrix A plus B whole transpose. So, we get A plus B whole transpose is equal to A transpose plus B transpose plus we see that A plus B whole transpose is equal to A transpose plus B transpose. Verified? This completes the session. Hope you understood the session. Take care and goodbye.