Assignment 10 - Due Thursday 11/17/2005
Read: Hubbard and Hubbard Section 2.3, 2.4. It is possible we may start on 2.5.
Exercises:
Hand in only the exercises which have stars by them.
Section 2.3 (pages 190-192): 2, 3, 3a*, 4, 5, 6, 7, 8, 9, 11
Section 2.4 (pages 204-206): 2, 2b*, 4*, 7, 8*, 9, 10, 11, 14*
Extra questions:
1*. Express the matrices in question 2.3.2b and 2.3.2c on page 190 as products of elementary matrices.
2. Suppose that
is a linear mapping between spaces of the same dimension. Prove that if f is 1-1 then f is onto. Prove conversely that if f is onto then f is 1-1. Comments on some exercises:
Some of the exercises in Section 2.4 seem too easy, like questions 3, 5 and 6 for example, and I have left them out of the recommended list. Others seem to require the reader to understand some very specific things which do not seem to me to be that instructive. I include questions 12 and 13 from Section 2.4 in this category, even though in the margin the authors suggest that question 12 is an important exercise. Have a look, and form your own opinion.
... and some more comments:
In the exam on November 10 the material will be taken from Sections 1.5 - 1.10, starting in Section 1.5 at page 94 where limits, continuity etc. of sequences of vectors and vector-valued functions are introduced, plus the extra questions on the assignment sheets. You may not use books or notes on the exam, but you may use a calculator.
There is a question on the exam in which you are asked to choose between a pair of statements (both are true statements) and prove one of them. If you can answer questions like 1.7.14 or 1.6.7 adequately you should be able to do this question. The difficulty may be that you do not have much experience answering this kind of question.
What we will do around Thanksgiving:
Mathematically, that is. Class will be cancelled on Wednesday 11/23. Homework Assignment 11 will be due on Tuesday 11/29, and I will hand it out Friday 11/18. I will also be away on Monday 11/14 and Wednesday 11/16, but class is not cancelled - you will be taught by someone else.