12. Do the following problem by hand. (a) In IEEE 754 double precision floating point arithmetic, m = 2-52 and d = 52 (see textbook page 12). Let e = m/4. Find fl(e) and fl(1/e') (b) Find the largest floating point number less than fl(1/). Show your work (c) Now let A What is the floating representation of the matrix A, fl(A)? (d) Using Gaussian elimination with double precision floating point arithmetic, find the LU factorization of fl(A) without pivoting. You will need to use the previous parts. (e) Still pretending you're a computer, compute the product of the factors you obtained above using floating point arithmetic. Com- pare with the original matrix A. What happened?