Question 1. Suppose A is a 3 3 matrix. 1. Find a 3 3 matrix Sij so that the product SijA is the same as the matrix A after applying the row operation Ri Rj . 2. Find a 3 3 matrix Tij (c) so that the product Tij (c)A is the same as the matrix A after applying the row operations Ri + cRj Ri . 3. Find a 3 3 matrix Ui(c) so that the product Ui(c)A is the same as the matrix A after applying the row operation cRi Ri . 4. Row reduce (by hand) the matrix A = 1 0 5 2 1 6 3 4 0 . Carefully keep track of the row operations. 5. Now replicate your row reduction from Part 4 by using the matrices that you found in Parts 1, 2, and 3. For example, if the first row operation you perform is to interchange rows 2 and 3, then you would multiply A on the left by S23 to get S23A. Do not evaluate the product, simply write out the matrices like U2(3)U3(1)T12(3)S23A. 6. Compute the product of the row-operation matrices that you found in Part (5). Do not include A in your product. So in the example above, you would compute the matrix product U2(3)U3(1)T12(3)S23. Call this matrix B. 7. What is the matrix B? Explain your answer.