**Math 3592H Honors Mathematics I Fall Semester 2003
**

Read:

Exercises (

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, 13*, 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.

In the exam on November 6 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 trouble will probably be that you do not have much experience doing this kind of question.