Exercise 1 LU decomposition [12 points] Note: This is a "pen and paper" exercise. All intermediate steps must be documented to receive credit. You can photograph or scan your handwritten notes. You can also type them up, if you want. a) Compute (by hand and without pivoting) the LU decomposition of the matrix A = 1 2 3 3 8 7 2 0 7 using Gaussian elimination, as discussed in the lectures. b) Check that you indeed recover A by explicitly multiplying L with U. c) Calculate the determinant of A using the LU decomposition. d) Solve the linear equation Ax = b, where b = 1 2 3 using the LU decomposition