Math 311 Exercises

Text: Richard E. Williamson and Hale F. Trotter, Multivariable Mathematics, 4th ed., Prentice-Hall, Englewood Cliffs, NJ, 2004.

Section   Exercises
1.1 9, 12, 14, 26, 28
1.2 25, 30, 32
1.3 3, 5, 13, 14, 18, 19
1.4 8, 15, 18, 21
1.5 13, 19, 27
1.6 7, 9, 16
2.1A 5, 9, 12
2.2C 9, 13, 19, 24, 28
2.2D 2, 4, 10, 11
2.3 6, 10, 17, 33, 39
2.4 8, 9, 19, 21, 23
2.5 5, 6, 8, 9, 11, 17, 18
3.1 3, 4, 7, 9, 10, 13, 19, 23, 24
3.2 7-11, 13, 26, 27, 30
3.3 6-8, 11, 15-17, 20, 24, 27
3.4 5-9, 13, 17, 19, 21
3.5B 3, 8, 10, 13, 17, 27, 35, 40, 41
3.5C 1, 3, 4, 11, extra problems 1, 2
3.6A 3, 5, 6, 8, 15, 17
3.6C 2, 3, 8, 11, 13, 16, 19, 21
3.7A 2-5, 7, 8, 11, 13
3.7B 3-5, 7, 8, 11, 12, 17
3.7C 1-3, 5
4.1D 3, 4, 12, 13, 14, 16, 19
4.4B 4, 5, 8, 9, 11, 14, 23
5.3 4, 7, 10, 13, 19, 20
5.4 1, 4, 9, 25, 26
6.2A 1, 2, 4, 8, 11
6.2B 2, 5, 9
6.5D 3, 4, 9, 11, 12
7.4D 21-23
9.1 3, 4, 9, 10, 17
9.3 5-7, 9, 12
9.4 5, 7, 9, 10, 12-14, 24
9.5 6, 8, 14, 18, 19, 20

Extra problems

  1. Let A be the matrix given below. Find the dimension of the image of A. Use it and problem 11, § 3.5C to find the dimension of the null space of A.
     1 -2  3  3
     2 -5  7  3
    -1  3  -4  3

  2. Suppose that B is a 7×10 matrix, and that the dimension of the null space of B is 5. What is the dimension of the image (column space) of B?

Updated 8/25/04 (fjn).