Assignment 3 Marking Scheme and TA Comments Question 1: Most students did very well on question 1. Some mistakes: - Didn't use permutation matrix at all, either in the LU factorization or computing Pb (-2 marks) - Errors in matrix multiplication (including use of permutation matrix) (-1 mark) - Not considering largest absolute value element when permuting rows for LU (-1 mark) - Unnecessary interchanging of rows (-1 mark) For part (b), as long as the students correctly did forward and back substitution full marks were awarded (even if LU with pivoting from part (a) was incorrect). -------------------------------------------------------------------- Question 2: The following is the marking scheme for Q2:    (a) 3 marks for correctly setting up the matrix A, 1 mark for setting up vector b, and 1 mark for correct value for f_hat    (b) 3 marks for correct error bound formula, 2 marks for correct matlab code (I took off 1 mark if there is any inconsistency in the norm used or incorrect calculation) -------------------------------------------------------------------- Question 3: I divided the 10 marks as follows: 4 marks for the code, 2 marks for formatted, reasonable results, 2 marks for discussion of condition number v.s. n, and 2 marks for discussion of correct digits v.s. condition number. 1. The students did quite well in the code part. 2. Some students didn't format the results well. I usually took 1 mark off. 3. Some students failed to answer the two requested sub-questions. They lost 2 marks for each. 4. Some students didn't get appropriate, reasonable and quantitative relationships for condition number v.s. n and correct digits v.s. condition number. I deducted 1 or 2 points depending on the quality of the answer.