Math 54 Discussion Section Problems
Mike Hartglass September 29, 2010
You should work on the following problems in groups of 3 or 4. Try to get through as many as you can, but you arent expected to nish everything. In fact, the answers are largely unimpor
Math 54 Discussion Section Problems
Mike Hartglass September 27, 2010
You should work on the following problems in groups of 3 or 4. Try to get through as many as you can, but you arent expected to nish everything. In fact, the answers are largely unimpor
Math 54 Discussion Section Problems
Mike hartglass September 22, 2010
You should work on the following problems in groups of 3 or 4. Try to get through as many as you can, but you arent expected to nish everything. In fact, the answers are largely unimpor
Math 54 Discussion Section Problems
Mike Hartglass September 20, 2010
You should work on the following problems in groups of 3 or 4. Try to get through as many as you can, but you arent expected to nish everything. In fact, the answers are largely unimpor
Math 54 Discussion Section Problems
Mike Hartglass September 15, 2010
You should work on the following problems in groups of 3 or 4. Try to get through as many as you can, but you arent expected to nish everything. In fact, the answers are largely unimpor
Math 54 Discussion Section Problems
Mike Hartglass September 10, 2010
You should work on the following problems in groups of 3 or 4. Try to get through as many as you can, but you arent expected to nish everything. In fact, the answers are largely unimpor
Math 54 Discussion Section Problems
Mike Hartglass September 8, 2010
You should work on the following problems in groups of 3 or 4. Try to get through as many as you can, but you arent expected to nish everything. In fact, the answers are largely unimport
Math 54 Discussion Section Problems
Mike Hartglass September 1, 2010
You should work on the following problems in groups of 3 or 4. Try to get through as many as you can, but you arent expected to nish everything. In fact, the answers are largely unimport
Math 54 Discussion Section Problems
Mike Hartglass August 30, 2010
You should work on the following problems in groups of 3 or 4. Try to get through as many as you can, but you arent expected to nish everything. In fact, the answers are largely unimportan
Math 54 Discussion Section Problems
Mike Hartglass August 27, 2010
You should work on the following problems in groups of 3 or 4. Try to get through as many as you can, but you arent expected to nish everything. In fact, the answers are largely unimportan
Math 54 Quiz 8
Mike Hartglass November 6, 2010
13 . Find matrices Q and D where Q is an or31 thogonal matrix, D is a diagonal matrix and A = QDQ1 .
1.) Consider the matrix A =
The characteristic polynomial is (t 1)2 9 so its roots are 2 and 4. For t = 2,
Math 54 Quiz 7
Mike Hartglass November 6, 2010
1 1 3 0 and 1 . 1.) Let W be the subspace of R spanned by the vectors 0 1 a.) Find an orthogonal basis for W . 1 1 Setting x1 = 0 and x2 = 1 using Gram Schmidt gives v1 = x1 and v2 = 0 1 0 0 1 2 ,v1 x2 x1 ,v
Math 54 Quiz 6
Mike Hartglass November 6, 2010
1.) Find P and D with P invertible and D diagonal such that A = P DP 1 or explain why this is impossible. 13 A= . 35 The characteristic polynomial for A is t2 6t 4 = (t 3)2 13 so we see that 2 13 3 it has roo
Math 54 Quiz 5
Mike Hartglass November 6, 2010
1.) Consider the matrix 120 A = 3 1 2 . 1 5 2 Find bases for the null space and the column space of A. 120 This matrix can be row reduced to 0 7 2 so by writing the appropriate aug000 mented matrix and solvin
Math 54 Quiz 2
Mike Hartglass September 17, 2010
1.) (3 points) Let S = cfw_, , ., be a subset of Rn . Without using the phrase v1 v2 vn linearly independent, dene what it means for the set S to be linearly dependent. The set S is linearly dependent exa
Math 54 Midterm 2 Review
Mike Hartglass November 7, 2010
1.) True/False: a.) If A is row equivalent to False b.) If A is diagonalizable then the columns of A are linearly independent. False 123 c.) The matrix 2 3 4 is diagonalizable. 345 True 110 d.) The
Math 54 Midterm 2 Review
Mike Hartglass October 31, 2010
1.) True/False: a.) If A is row equivalent to 10 04 then the eigenvalues of A are 1 and 4.
b.) If A is diagonalizable then the columns of A are linearly independent. 123 c.) The matrix 2 3 4 is diag
Math 54 Midterm 1 Review
Mike Hartglass September 26, 2010
1.) Let A denote the matrix 3 2 1 3 2 1 A= 0 1 1 Find bases for the following spaces: Col(A), Col(A2 ), Nul(A), Nul(A2 ). 2.) Determine if the following statements are true or false: a.) If A and
Math 54 Linear Algebra and Differential Equations Instructor: Dan-Virgil Voiculescu 105 Stanley MWF 3 - 4 Office: 783 Evans Office hours: W 4:15-5:30 , F 1:30 - 2:30 Midterm I W October 4 Midterm II W November 8 Final Tu December 14 7 - 10 p Grades: all g
Advance Assigned Reading Schedule Math 54 Fall 2010 Instructor: D.-V. Voiculescu L = Lay N = Nagle Saff Snider Week I 08/26 L 1.1.-1.3 L 1.4,1.5,1.7-1.9, 2.1 L 2.2,2.3,2.8,2.9 L 3.1-3.3 L 4.1-4.3 L 4.4,4.5,4.6 L 4.7, 5.1 L 5.2-5.4,6.1 L 6.2-6.5 L 6.7,7.1,
Homework Assignments Math 54 Fall 2010 Instructor D.-V. Voiculescu The assigned homework of a week is due at the second discussion section meeting of the following week. L = Lay Week L 1.1 5, 7, 13, 18, 22, 31 L 1.2 4, 8, 11, 19, 30 L 1.3 5, 10, 13, 25, 2
Due by 5pm on Friday Nov. 5th, 2010. You are encouraged to work in small groups for this assignment. Write your name AND your lab section on the problem set before submitting it.
1. Provide the major product or products that would be obtained for each of
Chern l 12A, Fall 2010 - Problem Set 3
Due in class on Oct. 28th, 2010. You are encouraged to work i n small groups for this assignment. Write your name AND your lab section on the problem set before submitting it.
1 . Classify each o f the following co
Due in class on Oct. 28th, 2010. You are encouraged to work in small groups for this assignment. Write your name AND your lab section on the problem set before submitting it.
1. Classify each of the following compounds as chiral or achiral. If they are ch
Due in class on Oct. 5, 2010. You are encouraged to work in small groups for this assignment.
1. Provide correct names for each of the following alkenes: a. b. c. d. I e. 2. Rank the following alkene isomers in terms of their thermodynami