Math 167 homework 1 solutions
October 6, 2010
1.3.14a: Construct a 3 by 3 system that needs two row exchanges to reach
a triangular form and a solution. There are many examples, but this is one:
3y 2z
150A Algebra
Monica Vazirani November 3, 2010
Midterm
Name:
ID:
Section:
1. (10 points) In parts (a)(b), give a careful denition of the terms in boldface. It is set up in
several cases that you can j
Math 150A  Fall 09  Homework 9 Selected Solutions
(Based on solutions prepared by Je Ferreira )
5.4.1 Prove that a discrete group G consisting of rotations about the origin is cyclic and is generate
Math 150A  Fall 09  Homework 7&8 Selected Solutions
(Based on solutions prepared by Je Ferreira )
2.10.1 Let G be the group of invertible real upper triangular 2 2 matrices. Determine whether or not
Math 167 homework 3 solutions
October 20, 2010
2.1.22: For which righthand sides (nd a condition on b1 , b2 , b3 ) are these
systems solvable?
(a)
1
4
2
x1
b1
2
8
4 x2 = b2
1 4 2
x3
b3
r2 2r1 and r3
Math 150A  Homework 3 Selected Solutions
(Based on solutions prepared by Je Ferreira )
2.3.2 Prove that the products ab and ba are conjugate elements in a group G.
Proof. Wee need to show the existe
Math 167 homework 2 solutions
October 13, 2010
1.5.44: Find a 3 by 3 permutation matrix with P 3 = I
Find a 4 by 4 permutation matrix with P with P 4 = I .
0010
001
1 0 0 0
P = 1 0 0
P =
0 1 0 0
010
Math 228A
Homework 2
Due Friday, 10/22/08, 4:00
1. Use the standard 3point discretization of the Laplacian on a regular mesh to nd a numerical
solution to the PDEs below. Perform a renement study usi
Math 228A
Homework 1
Due Tuesday, 10/12/10
1. Let L be the linear operator Lu = uxx , ux (0) = ux (1) = 0.
(a) Find the eigenfunctions and corresponding eigenvalues of L.
(b) Show that the eigenfuncti

cos20
sin20
By trig, the translation vector is 2a sin0(sin0, cos0), which is orthog to (cos0, sin0).
Also, note, above, any q on line L would give us the same translation vector (nothing
special a