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Last updated 11/18/02 12:20 p.m.
MCS-221 Problem Assignments: Fall 2002
| Section
| Practice problems*
| Problems to turn in
| Due date
|
| 4.1
| 1
| 2, 10
10(a) Not 1+2x+3x^3 but 1+2x+3x^2
| T 11/5
|
| 4.1
|
| 3
3(c) Make X= [x,y,z]^t.
| F 11/8
|
| 4.2
| 3
| 1,2
| F 11/8
|
| 4.2
| 5, 9, 12
| 8, 10
| T 11/12
|
| 4.4
| 1,2,11
| 4,5, Rigid motions proofs
(ps)
(pdf)
| T 11/12
|
| 4.5
| 1, 3, 5, 7, 8, 10
| 4
| F 11/15
|
Fundamental
Theorem, II
| Study proof.
| Fredholm's Alternative
(ps)
(pdf)
| R 11/21
|
| Test 4
|
|
| M 11/18
|
* 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.
Homework rules
- 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.
Proof Portfolio (Perfect Proofs)
- 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.
Proofs
- 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.