MCS-221 Problems: Fall 2002

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Last updated 11/19/02 12:10 p.m.

MCS-221 Problem Assignments: Fall 2002

Section	Practice problems*	Problems to turn in	Due date
Fundamental Theorem, II	Study proof.	Fredholm's Alternative (ps) (pdf)	F 11/22
5.1	1	1 (modified: add 1's to 1st rows) Write 4x4 det A as sum of 4! products.	F 11/22
5.2	1-5	6 (Vandermonde), 12, 13, 14	T 11/26
5.3	3	1, 4	T 11/26

* These are merely some suggested problems. You should work as many problems as necessary to master the ideas.

Unless otherwise indicated, the problems are from our text, Linear Algebra: Ideas and Applications, by Richard Penney.

Acknowledge your sources (people and texts).
In nontrivial problems, show how you get your answers.
Turn in neat, well-written solutions, not messy first drafts. Trim "fringes." Staple.
Do not copy collaborative solutions; write up solutions in your own words.
Turn in homework on time. Each class day late reduces the possible points by 25%.
Do extra credit problems entirely on your own.

Problem 1.1 #9
Problem 1.2 #22
Problem 2.2 #10
Problem 3.3 #18
Let V and W be vector spaces. Let T: V -> W be a linear transformation. Let U be a subspace of V. Prove: (a) T(U) is a subspace of W; (b) T^-1({0}) is a subspace of V.
Problem 4.2 #12 (The reference should be to Exercise 10.)
Problem 4.2 #13

Proofs should be written in complete sentences. Mathematical expressions should be embedded in a grammatically sensible way. Look at your math texts to see how this is done.
Every step in a proof is or can be justified by a reason. Valid reasons include assumptions, definitions, and previously established results. The extent to which reasons are omitted and proofs abbreviated depends on the audience.