Calculus and Linear Algebra Review Problems

1. Let . Compute .
2. In what direction is increasing most rapidly at ?
3. Define where F is a differentiable function. Compute .
4. Find and classify all critical points of and of .
5. A rectangular box whose edges are parallel to the coordinate axes is inscribed in the ellipsoid . What is the greatest possible volume for the box?
6. Are the vectors

   

   linearly dependent or independent? Are these vectors a basis for R?

7. Find the inverse of the matrix

   

8. Let A and B be invertible matrices. What is the inverse of their product, AB?
9. Define . Compute , , and when

   

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