MATH
21 B
Mathematics Math21b Fall 2010
Linear Algebra and Differential Equations
Exhibit: first midterm mistakes
Course Head: Oliver Knill
Office: SciCtr 434


Here are a few common mistakes or reasons to lose points for the first midterm:
  • Row reduction errors: a common pitfall was to do many steps at once and then trip up with a numerical error or do something like in this illustration:
            | 1  1  1 |         | 0 0 0 |     | 2 3 4 |
            | 1  1  1 |         | 0 0 0 |     | 0 0 0 |
            | 2  3  1 |         | 2 3 4 |     | 0 0 0 |
            
    where in the first step, the second row is subtracted from the first and simultaneously the first from the second.
  • No work shown. However simple the argument, we need to see some work or reasoning. The problems with "no explanation needed" were indicated. The reason why a work trail should be seen is that sometimes also incorrect arguments can lead to correct solutions.
  • In problem 6) a last line
            0    0    0    1   |    0
            
    would sometimes be interpreted as that the system is inconsistent. The 1 would have to be in the last column to become a problem.
  • A major difficulty was to find the B matrix in a coordinate change problem. The B matrix tells what the matrix does in the basis vectors. For example, if v2 goes to v3, this means that T(v2) = 0 v1 + 0 v2 + 1 v3 meaning that the vector [0,0,1] (written as a column vector) makes the second column of B.


Please send questions and comments to math21b@fas.harvard.edu
Math21b (Exam Group 1)| Oliver Knill | Fall 2010 | Department of Mathematics | Faculty of Art and Sciences | Harvard University