Information on Midterm 2, Math 203

1. Find a basis and the dimension of each of the four fundamental subspaces of a given matrix.

2. Given are two vectors. Find their angle. Also find all vectors that are orthogonal to both of the given vectors.

3. This is another spy problem (similar to Problem 48), where linear transformations are used to encrypt messages.

4. One little proof of a statement similar to the ones given in Problem 55. If you know what you do you won't need more than a line for this proof.