Mathematics 2122-001
Calculus for Life Sciences II
Fall 2002
Study Guide for Test #4
Instructor: Dr. Alexandra Shlapentokh

1. Solve for if and .
2. Solve for if , and .
3. Solve for if , and .
4. Solve for if and .
5. Solve for if and .
6. Draw the sum of the following vectors.

7. Draw the sum of the following vectors.

8. Let and be points with coordinates (1,2) and (3,4) respectively. What are the coordinates of the position veector equal to ?
9. Let be position vectors with coordinates and respectively. Then what are the coordinates of a positional vector equal to
(a) ?
(b) ?
(c) ?
(d) a unit vector in the direction of ?
(e) a vector of the same length as but pointing in the opposite direction?
10. Let be a positional vector whose polar coordinates are . What are Cartesian coordinates of ?
11. Let be a positional vector with coordinates . Then
(a) what is the length of ?
(b) what angle does make with the positive direction of -axis?
(c) what is if a positional vector is parallel to ?
12. Consider the matrix


(a) What are the dimensions of ?
(b) What is ?
13. Let

What is ?
14. Does the product exist?
15. Let

What is ?
16. Rewrite the following system in the matrix form.








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