M A T H 2 1 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