Just Exercise 1.8.15. please. I have included the other pages just in case you need it for reference. Thank you.

Exercise 1.8.15 Write a Fortran program and subroutines to solve linear systems Ar by Gaussian elimination with partial pivoting. Your subroutines should be column riented. Try out your program on the test problems Ar b and Az-, where 50 52 14 b12 51 15 2 10 8 8 6 1 4 -2 41 A- 0 2 3 2 1 c= | 121. 3 8 3 10 9 48 12 Afer the decomposition your transformed marix should be 2/3 14/3 6 10 4/3 0 0 1/3 2/7 4/11-20/11 -6/11 The row interchanges are given by intch 4, 4, 4, 5, 5). The solution vectors are (1, 2, 1, 2, 1]" and [2, 1, 2, 1, 2. Once you have your program working this problem correctly, try it out on some other problems of your own devising. Programming Gaussian Elimination Exercise 1.8.12 Write an algorithm that implements Gaussian elimination with partial pivor- ing. Store L and U over A, and save a record of the row interchanges. Your solution to Exercise 1.8.12 should look something like this: Gauss (A, n, intch, flag) clear flag for k 1,2,...,n -1 if (amax = 0) then set flag intch() - o } (A is si (A is singular) (As singular) else [1n smallest integer k for which lam (record row interchange) = arnaz intch(k) m if (m k) then . interchange rows k and m, including multipliers akask/akk calculate multipliers subtract aik times [akk+,ak,n) for i-k+1,... ,n for i=k+1, ,n (row operations) from (ai,k+1,.. ,ai,n] if (ann = 0) then set flag inten(n) 0 (A is singular) else [ intch(n)-n ] A main program to drive the subroutines Gauss and Solve might be organized something like this: read n and A call Gauss (A, n, intch, flag) if (flag is set) then print 'coefficient matrix is singular stop read num (number of right-hand sides) for m 1,... , num read b call Solve (A, b, n, intch, flag) Lprint 'solution number' m 'is' b (prints solution)