Question 1. Suppose A is a 3 x 3 matrix. 1. Find a 3 x 3 matrix S,; so that the product S,; A is the same as the matrix A after applying the row operation R. + RJ- 2. Find a 3 x 3 matrix T.;(c) so that the product Ty (c) A is the same as the matrix A after applying the row operations R, + CR, -> R. 3. Find a 3 x 3 matrix U,(c) so that the product U.(c) A is the same as the matrix A after applying the row operation CR, - R. 4. Row reduce (by hand) the matrix 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 mul- tiply A on the left by Sas to get $23A. Do not evaluate the product, simply write out the matrices like U2(3)Us(-1)T12(-3)$23A. 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)Us(-1)T12(-3)$23. Call this matrix B. 7. What is the matrix B? Explain your answer. Numeracy 2. As the CEO of Gilmore's Glorious Goods you have been allocated an operating budget for the year. The company consists of two executive departments, each department is run by three directors, each director has four project managers, and each project manager is working on five projects. If each project has precisely one project O FiCO N 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 mul- tiply A on the left by Sas to get $23 A. Do not evaluate the product, simply write out the matrices like U2(3)Us(-1)T12(-3) $23 A. 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)Us(-1)T12(-3)$23. Call this matrix B. 7. What is the matrix BY Explain your answer. Numeracy 2. As the CEO of Gilmore's Glorious Goods you have been allocated an operating budget for the year. The company consists of two executive departments, each department is run by three directors, each director has four project managers, and each project manager is working on five projects. If each project has precisely one project manager, and the budget is to be evenly divided amongst every project, what percentage of the budget does each project receive? Numeracy 3. Suppose we define a function on the natural numbers, where f(0) = 1 and f(n) = nf(n - 1) for n 21. 1. Compute f(1). f(2). f(3). . .. . f(10) (using a calculator as necessary). 2. Find a closed form expression for f(n): that is, a way of computing f(n) without having to compute f(n - 1). Use this to compute f(100). 3. If n and k are natural numbers with &