Lectures and Homework 642:550, Summer 2003


The exercises listed here should be prepared for the second class following the one in which they are assigned. Problems will be listed here shortly before they are announced in class. A table of assigned problems will evolve in this space.

Date Section Pages Problems
Jun 23 3.6 205 - 207 14 (both parts from text and extra part from S1).(see note)
S1 7 A.
Jun 24 4.2 218 - 221 6, 11 (see note).
4.3 228 - 230 4.
4.Review 241 - 242 3, 13, 16 (see note).
Jun 26 5.1 251 - 253 5, 16.
5.2 260 - 261 2, 3 (see note), 7.
Jun 30 3.Review 208 - 210 28.
5.3 272 - 274 8
S4 4 1, 2.
Jul 01 S5 4 1, 2, 3.
Jul 03 5.4 286 - 289 20.
5.Review 319 - 321 1, 6.
S6 6 1, 2, 3, 4.
Jul 07 S7 4 1 (see note), 2, 3.
Jul 08 5.5 301 - 303 6, 7.
5.Review 319 - 321 15.
Jul 10 S8 9 1, 2, 3, 4, 5.
Jul 14 S9 4 1, 2.
7.2 369 4, 10 (see note).
Jul 15 7.3 378 - 379 1, 5.
7.4 386 - 387 5 (see note).
Jul 17 6.2 337 - 338 2, 7.
Jul 21 6.3 345 - 346 1, 2, 11.
6.4 352 - 354 11 (see note).
Jul 22 Appendix A 451 - 452 2, 4.
nothing more yet

Notes

3.6.14
The desired factorization is the reduced factorization described in item 2 on page 197. More details and an extra part are in Supplement 1. There is a misprint in the textbook: the number of columns of L that must be dropped is m-r (matching the rows of U that are discarded), not n-r (as written in the text). [This was noticed by a student in this class].
4.2.11
One part asks to use properties of the determinant to show that the determinant of  every 3 by 3 skew-symmetric matrix is zero.  Another part asks for one example of a 4 by 4 skew-symmetric matrix with nonzero determinant.  This example should be a numerical matrix, and you should find the determinant to be sure that it isn't zero.
4.R.16
The matrix A must be n by n in order to have a determinant. The answer will depend on n, and should be found by direct calculation for n=1, 2, and 3. Do more cases only if you need them to find a general method.
5.2.3
The two diagonalizing matrices should be essentially different. The rescaling mentioned in Remark 2, and permutation of columns of S, which should have been mentioned there, are always available. Since the matrix A of this problem is diagonalizable in spite of having a repeated eigenvalue, additional diagonalizing matrices are available. At least one column of your second S should not be a multiple of any column of your first choice of S.
S7.1
It was intended that this matrix arise in the middle of the calculation instead of being give. You should change the diagonal to 17 and -25 and then quickly reduce to the matrix that was written..
7.2.4 and 7.2.10
A little more information on the maximum norm is in Supplement 9. These problems should be done using both the Euclidean norm and the maximum norm to get condition numbers. Then, you should explain any differences.
7.4.5
Matrix A was introduced in problem 4 and Gershgorin's theorem is stated on page 386, just before that problem.
6.4.11
This problem uses a simple form of Remark 2 on page 352.

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