3. (LU decomposition, 14pt) You are given the matrix and you want to find an LU-decomposition A=LU as follows: a) [6pt] Perform forward elimination on A (so only until A is in upper triangular form); explicitly state the (six) elementary operations you are performing, and show the intermediate states of A. Note: You do not need elementary matrices for this problem. You don't have to show all intermediate states of A, one for each column you process is fine. b) [1pt] State the resulting U. c) [3pt] State L (based on the elementary operations). d) [1pt] Verify that A=LU. e) [3pt] Compute the determinant of A based on the LU-decomposition you got in a). Show how. Hint: you can verify using det(), but you need to work with the LU-decomposition to get the result