(f) 1 2 A=0 0 0 32 1 with the same right-hand side as before. 12. The Cholesky algorithm given on page 116 has all those wretched loops as in the Gaussian elimination algorithm in its simplest form. In view of Section 5.4 and the program ainvb we should be able to achieve also the Cholesky decomposition effect more efficiently. Write a code implementing the Cholesky decomposition with only one loop (on k), utilizing outer products. 13. The script in Example 5.13 will give different answers each time you run it, because the random number generator starts at different spots. Please fix this, making the program having the option to run on the same input when reinvoked. (Check help randn to see how to do this.) Run the program for n = 200 and n = 500. What are your observations?