Assignment 10 - Due Thursday 11/13/2008
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 180-182): 2, 3, 3b*, 4, 5, 6, 7, 8, 9, 11
Section 2.4 (pages 193-194): 2, 2b*, 4*, 7, 8*, 10, 12*
Extra questions:
1*. Express the matrices in question 2.3.2b and 2.3.2c on page 180 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 question 11 from Section 2.4 in this category. Have a look, and form your own opinion.
... and some more comments:
In the exam on November 6 the material will be taken from Sections 1.5 - 1.10, starting in Section 1.5 at page 89 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 (on page 139) or 1.6.7 (on page 119) 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.