Math 110

Here are solutions to homework assignment 4.

KEY CONCEPTS:

chapter 1:

definitions of vector spaces/subspaces;
linear combinations, linear dependence/independence;
bases, spans, dimensions of spaces;

chapter 2:

linear transformation, null space, range, rank;
matrix represenation of a linear tranformation, writing matrix of a lin. transformation in different bases;
composition of linear transformations, matrix multiplication;
invertability, isomorphisms;
change of coordinate matrices;

chapter 3:

elementary row/column operations and their properties (not changing the rank of a matrix, etc.), row echelon form;
rank of a matrix (all equivalent definitions, e.g. maximum number linearly independent columns/rows, dimension of the space spanned by columns/rows, and many more) and its properties (e.g. rank(A) = rank(AQ), if Q is invertible, and many more), inverse of a matrix;
systems of linear equations -- underdetermined, overdetermined, consistent/inconsistent, dimension of solution space, reduced row echelon form -- everything :)

chapter 4:

determinants, their properties, area of a parallelogram

PRACTICE PROBLEMS:

You are not required to solve/write down all the problems below. The problems are to help you practice for the midterm. Make sure you know how to do them.

section 1.2: #1, 13, 14, 17
section 1.3: #10, 13, 15
section 1.5: #1, 2, 8
section 1.6: #1, 4, 13, 15, 31, 32

section 2.1: #1, 9, 10, 11, 17
section 2.2: #1, 2, 3, 9, 10
section 2.3: #1, 3, 12
section 2.4: #1, 3, 6, 7
section 2.5: #1, 2, 3, 4

section 3.1: #1, 12
section 3.2: #1, 2, 3, 6
section 3.3: #1, 2, 3, 8
section 3.4: #1, 2, 3, 4, 6, 10, 12

section 4.1: #1, 4, 5, 6, 7, 8

Zachary Judson: Thursday (TODAY), September 30th, 6-8 pm, 70 Evans

Tom Dorsey: Saturday, October 2nd, 3-6 pm in 60 Evans (sections 103, 104)

Luiza Miranian: Friday, October 1st, 2-4 pm in 433 Latimer (sections 107-108)
(Please, come prepared, with specific questions and problems you would like to see explained.
Review session will be not a lecture, but interactive question/answer session. No questions - no answers :)

Graded homeworks 1, 2, 3, 4 are outside of 1093 Evans. The following comments on the homeworks:

1) In true/false questions, make sure to include your reasoning: if the answer is false - provide a counterexample, if true - explain why. For blank T/F answers no credit is given

2) Neatly written, well organized and STAPLED homeworks are greatly appreciated. Writing things up accurately often helps to organize your thoughts and improves understanding.

section 4.2: 1, 10
section 4.3: 5
section 4.4: 1, 4(g,h)

Here are solutions to homework assignment 3.

Here are solutions to homework assignment 2.

Here are solutions to homework assignment 1.

3.3: 1(all), 2(def), 3(def), 6, 7(ace), 8, 10
3.4: 1(all), 3, 5, 6
4.1: 1(all), 3(b), 4(c)

2.4: 2(acf)
2.5: 6, 8, 10
2.6: 1(all), 3 (both), 5, 8
3.1: 1(all), 2, 9
3.2: 1(all), 2(efg), 7, 14

It should be handed in to your GSI.

First week (due Monday, September 13)
1.6: 1, 5, 8, 14
2.1: 13, 17, 26
2.2: 1(all), 2 (a,c,f), 4, 5
2.3: 1(all), 3, 8

I will not be assigning "readings". You should read all sections in the book for which there is homework assigned. Thus, in chapter 1 read sections 1,2,3,4,5,6 and in chapter 2 read fairly soon sections 1,2,3.

sect 1.1, 3b,d,7
sect 1.2, 1(all),18,21
sect 1.3, 9,11
sect 1.4, 10,11
sect 1.5, 1,3,7,10
Exams: First midterm, October 5, in class; second midterm, November 9, in class; final exam, Friday, December 17, 12:30-3:30pm

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