Math 2901: Homework 9
MENU, Fall 2012
NOT TO BE TURNED IN
Section 7.5. 13, 16, 24, 25, 29, 49, 50
Be sure to show and explain your work as best you can!
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Northwestern UniversityStudent ID:
Math 2901 Midterm 2
Autumn Quarter 2011
Wednesday, November 16, 2011
(2 points) Put a check mark next to your section:
Cutrone
Cyr 10am
Cyr 12pm
Gutzwiller 10am
Gutzwiller 12pm
Dont Know
Instructions:
Question Pos
Name:
Northwestern UniversityStudent ID:
Math 2901 Midterm 2
Autumn Quarter 2012
Monday, November 19, 2012
Put a check mark next to your section:
Allen
Canez
Cyr (10am)
Cyr (12pm)
Peters
Instructions:
Question Possible Score
points
1
16
2
16
3
14
4
14
5
North western Umversrtysgg; We)
t ID:
Math 2901 Midterm 2
Autumn Quarter 2012
Monday, November 19, 2012
Put a check mark next to your section:
Instructions:
0 Read each problem carefully.
Question Possible 0 Write legibly.
0 Show all your work on th
: ' . . Name:
North western Umversrty Student ID:
Math 2901 Practice Midterm 2
1. Determine whether each of the following statements is TRUE or FALSE. Justify your
answer.
(a) Let A, B, C be n X n matrices. If A is similar to B and B is similar to C, th
Math 2902: Homework 1
Northwestern, Winter 2014
Due: January 13, 2014
Bretscher, Section 5.1. 8, 9, 11, 16, 17, 25, 26, 28, 29, 32
TF. Is it true or false that there is an orthonormal basis of R3 which contains the vector
1
3
1
1
1
?
ASN. Say that v1 and
Math 2902: Homework 2
Northwestern, Winter 2014
Due: January 17, 2014
Bretscher, Section 5.1. 33, 35, 38, 39, 44
Bretscher, Section 5.2. 3, 6, 13, 32, 33, 35, 39
TF. Suppose that Q is a square matrix with orthogonal columns. Is it true or false that QT Q
Math 2902: Homework 3
Northwestern, Winter 2014
Due: January 24, 2014
Bretscher, Section 5.3. 3, 4, 8, 10, 28, 29, 35, 40, 42, 65.
For 28, instead of using the books hint (its ne if you do use it) recall that I outlined a way in
class to approach this, u
Notes on the GramSchmidt Process
MENU, Winter 2013
Im not too happy with the way in which the book presents the GramSchmidt process, and
wanted to provide some clarications as well as an alternate approach. First, recall the goal of the
GramSchmidt pro
Math 2902: Homework 5
Northwestern University, Winter 2014
Due: February 10, 2014
Colley, Section 1.4. 9, 10, 13, 19, 24, 25
Colley, Section 1.5. 3, 8, 12, 13, 21, 23, 28, 32
TF. Suppose that A is a symmetric 3 3 matrix and that u and v are two nonparall
Math 2902: Homework 9
Northwestern University, Winter 2014
Due: March 10, 2014
Colley, Section 2.6. 17, 20, 22, 24
Colley, Section 4.1. 9, 13, 18, 22
Colley, Section 4.2. 5, 12, 18, 22, 37, 41
TF. Say that P is a point on the surface xyz = 8. Is it true
. . ; Scuff N
' . Northwestern Unwersyim ID: 10 5
Math 2901 Final Exam
Autumn Quarter 2012
Wednesday, December 12, 2012
Put a check mark next to your section:
Instructions:
0 Read each problem carefully.
 Write legibly.
0 Show all your work on the
ame:
11}, g I N
Northwestern Urnversuyst
udent ID:
Math 2901 Midterm 2
Autumn Quarter 2012
Monday, November 19, 2012
Put a check mark next to your section:
Instructions:
I Read each problem carefully.
0 Write legibly.
I Show all your work on thes
Northwestern University
Name:
Student ID:
Math 2901 Practice Midterm 1
Fall Quarter 2010
Wednesday, October 20, 2010
Question 1. Complete the following denitions:
(a) A matrix is in echelon form if it has the following three properties:
(b) A set of vect
Practice Problems for Midterm 2
1. True/False
Determine whether each of the following is true or false. Briey justify.
1
(1) 0 is in the kernel of
0
0 2 4 5
6 3 8 10
12 4 1 3
0
(2) 0 : 1 z 1 is a subspace of R3 .
z
(3) If the vectors v1 , . . . , vn
Northwestern University
Name:
Student ID:
Math 2901 Practice Midterm 2
1. Determine whether each of the following statements is TRUE or FALSE. Justify your
answer.
(a) Let A, B, C be n n matrices. If A is similar to B and B is similar to C, then A is
sim
Math 2901: Quiz 4
MENU, Fall 2012
November 1, 2012
Name:
Suppose that v1 , v2 , and v3 are three linearly
matrix having these vectors as columns:

A = v1

independent vectors in R5 and let A be the 5 3


v2 v3 .


Find, with justication, the reduce
Math 2901: Quiz 4 Solutions
MENU, Fall 2012
Suppose that v1 , v2 , and v3 are three linearly
matrix having these vectors as columns:

v1
A=

independent vectors in R5 and let A be the 5 3


v2 v3 .


Find, with justication, the reduced rowechelon
Condensed Lecture Notes (Part 3)
Properties of the Chemical Elements
Hydrogen
Hydrogen is the most abundant element in the universe. It is a transparent gas under normal conditions.
It can form both a cation (H+) and an anion (H).
It is made industrially
Math 2901: Quiz 5
MENU, Fall 2012
November 8, 2012
Name:
Let T : R2 R2 be the linear transformation dened by
T (x) =
1 2
x.
4 3
Find a basis B = cfw_v1 , v2 of R2 such that the matrix of T relative to B is
basis youre looking for by
a
c
v1 =
and v2 =
.
Math 2901: Quiz 5 Solutions
MENU, Fall 2012
Let T : R2 R2 be the linear transformation dened by
1 2
x.
4 3
T (x) =
Find a basis B = cfw_v1 , v2 of R2 such that the matrix of T relative to B is
basis youre looking for by
a
c
v1 =
and v2 =
.
b
d
5 0
0 1
.
Math 2901: Quiz 6
MENU, Fall 2012
November 15, 2012
Name:
Compute the determinant of the following matrix:
1 2 5
0 0
3
A=
2 6 7
5 0
4
2
0
5
4
Based on your answer, how do you know that for any y in R4 there are scalars c1 , c2 , c3 , c4 such
that
Math 2901: Quiz 6 Solutions
MENU, Fall 2012
Compute the determinant of the following matrix:
1 2 5
0 0
3
A=
2 6 7
5 0
4
Based on your answer, how do you know that for any
that
2
1
5
0
0
3
c1 + c2
2
6 + c3 7
5
0
4
Solution. We do a cofactor expansi
Math 2901: Quiz 7
MENU, Fall 2012
November 29, 2012
Name:
Determine, with justication, the value(s) of k for which the following matrix is diagonalizable.
0 0 3
A = 3 k 3
1 0 2
Math 2901: Quiz 7 Solutions
MENU, Fall 2012
Determine, with justication, the value(s) of k for which the following matrix is diagonalizable.
0 0 3
A = 3 k 3
1 0 2
Solution. The characteristic polynomial of A is (using a cofactor expansion along the seco
Math 2902: Homework 8
Northwestern University, Winter 2014
Due: February 28, 2014
Colley, Section 2.4. 13, 22, 26, 28
Colley, Section 2.5. 2, 5, 8, 13, 23, 29
Colley, Section 2.6. 5, 8, 11, 12
TF. Suppose that f (x, y) is a function of two variables and
Name:
Northwestern UniversityStudent ID:
Math 2902 Practice Midterm 1
Winter Quarter 2013
Math 2902 Practice Midterm 1
Winter Quarter 2013
Page 2 of 9
1. Determine whether each of the following statements is TRUE or FALSE. Justify your
answer.
1