The exam will be during class (50 minutes) on Friday, Feb 25, 2000. The four problems will be as follows:

1. Solve a system with three unknowns and three equations using the LDU Decomposition of the matrix.

2. Given two explicit matrices A (2 by 2) and B (2 by 3), find the transpose of B, the inverse of A, the product of A and B, and so on.

3. Decide whether two given sets are subspaces.

4. Find the four fundamental subspaces of a given matrix, as well as bases for them and their dimensions.