In article <email@example.com>, Anonymous wrote:
>I already bought the text, the Cliff's >Notes guide to linear algebra, a 2003-version of the Schaum's outline, >and I even have an old 1968 version of Schaum's that my grandmother >used when she majored in math.
This is not your grandmother's Linear Algebra course! (I've always wanted to say something like that.)
>Maybe, if it isn't too much to ask, would anyone here be willing to >post some problems relating to mappings/kernel/image/isomorphims >and/or eigenvalues/eigenvectors, and I can attempt to solve them with >your help?
Sample question (a) Prove that the set M of all n by n matrices is a vector space (using familiar matrix addition and scalar multiplication.) What is its dimension? (b) Prove that the map f(x) = x^t is a linear transformation from M to M What is its kernel? (c) Compute the eigenvalues of f and find the eigenspaces.
I am of course deliberately choosing a question which emphasizes the proper use of terminology and abstraction, but this is a perfectly reasonable exam question. (IMHO -- but I have a reputation for thinking "interesting" questions are reasonable so maybe you shouldn't trust me.)