The exam will be during class (50 minutes) on Friday, Apr 21, 2000. The four problems will be as follows:

1. Given are three vectors w1, w2, and v. Find the lengths of w1 and w2, their inner product, the distance between them, the angle between them, and the orthogonal complement of W=L(w1,w2). Is v in W perp? Is v in W? Find the orthogonal projection of v onto W, as well as the minimal distance from v to W.

2. This is a least square problem.

3. Compute the determinant of a given 4 by 4 matrix by a cofactor expansion along the fourth row.

4. Find all eigenvalues and corresponding eigenvectors for a given 2 by 2 matrix.