Linear Algebra and its Applications
Dr. Elena Devdariani
Carleton University
January 11, 2014
Dr. Elena Devdariani (Carleton University)
Linear Algebra and its Applications
January 11, 2014
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1
C
The Cultural Literacy of
Graduate Management
Students
Richard P. Vance, Brooke A. Saladin, Robert W. Prichard, and Peter R. Peacock
T
he acrimonious
debate over
multiculturalism
in education has not y
Linear Algebra and its Applications
Dr. Elena Devdariani
Carleton University
February 4, 2014
Dr. Elena Devdariani (Carleton University)
Linear Algebra and its Applications
February 4, 2014
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1
C
Linear Algebra and its Applications
Dr. Elena Devdariani
Carleton University
January 26, 2014
Dr. Elena Devdariani (Carleton University)
Linear Algebra and its Applications
January 26, 2014
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1
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Linear Algebra and its Applications
Dr. Elena Devdariani
Carleton University
January 20, 2014
Dr. Elena Devdariani (Carleton University)
Linear Algebra and its Applications
January 20, 2014
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1
C
Linear Algebra and its Applications
Dr. Elena Devdariani
Carleton University
January 14, 2014
Dr. Elena Devdariani (Carleton University)
Linear Algebra and its Applications
January 14, 2014
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1
C
March 13, 2013
1
TEST 4 SOLUTIONSMATH 1102
/3
1. Suppose A Mnn (C) and C is an eigenvalue of A. Provide the
denition of an eigenvector corresponding to .
Solution: A vector v Cn is an eigenvector corr
November 5, 2012
1
SOLUTIONS TO TEST 2MATH 1102
1. Suppose the matrix
1
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
2
1
1 3
2 6
0
0
0
0
0
0
is the RREF of the augmented matrix of a system of linear equations
over C
Linear Algebra and its Applications
Dr. Elena Devdariani
Carleton University
March 22, 2014
Dr. Elena Devdariani (Carleton University)
Linear Algebra and its Applications
March 22, 2014
1 / 29
1
CH.6
Assignment 5Algebra I
Due at the beginning of tutorial Oct 30
1. Suppose
/3
1 2 1 1
2 0 1
A = 1
2 4 1 0
Compute a set of vectors in C4 whose span is equal to N (A). You may
use Theorem SSNS on page 11
Assignment 2 MATH 1102
Due at the beginning of tutorial Sep. 28th
1. Compute the standard form of the complex number
( 2 + i)( 2ei/4 )
.
3
i
2
/4
As always, show your reasoning.
2. Prove that
/3
(1 +
Media Literacy Online Project - Serving Educators Around The World
Media Literacy Review
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Mass Media a
Are You Culturally Literate?
Is this what every American needs to know?
Posted May 23, 2011
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James Franco GiftedHere is a short test of your cultural literacy. Are you able to p
A First Course in Linear Algebra
Robert A. Beezer
University of Puget Sound
Version 3.40
Congruent Press
Robert A. Beezer is a Professor of Mathematics at the University of Puget Sound,
where he has b
Cultural Literacy for College Students
Jeremiah Reedy
n article by Lois Roman, which appeared in the 25 December 2005 issue of the
under the title ,T,
Literacy of College Graduates Is on Decline:
Surv
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Assignment 11Algebra I
Due at the beginning of tutorial Jan. 29
1. Let X be a nonempty set and F be a eld. Dene F (X, F ) to be the set
of all functions from X to F , i.e.
/6
F (X, F ) = cfw_f : X F .
February 6, 2013
1
TEST 3 SOLUTIONSMATH 1102
1. Let F be a eld and A Mnn (F ).
/3
(a) Provide the denition of the determinant of A for n 2.
n
det(A) = j =1 (1)1+j [A]1j det(A(1|j )
/4
(b) Let F = Z3 a
Assignment 8Algebra I
Due at the beginning of tutorial Nov. 27
1. Compute AB where
/3
1
2
A=
and
0
1
B=
2
2
2
2
M22 (Z3 )
1
0
M23 (Z3 ).
Show enough work to convince your marker that you know what y
Assignment 2 MATH 1102
Due at the beginning of tutorial Oct. 2
1. Compute the standard form of the complex number
( 2 + i)( 2ei/4 )
.
3
i
2
/4
2. Prove that
/4
n
(1 + i)n = 2 (cos(n/4) + i sin(n/4)
fo
Assignment 13Algebra I
Due at the beginning of tutorial Feb 26
1. Suppose F is a eld and A Mmn (F ). Recall that the row space R(A)
of A is the span of the row vectors of A. It is a subspace of F n (t
Assignment 3Algebra I
Due at the beginning of tutorial Oct 16
1. Find the solution set to the following system of three linear equations /6
in three unknowns over C by rst placing its augmented matrix
Assignment 9Algebra I
Due at the beginning of lecture Dec. 3
1. Suppose F is a eld and A Mnn (F ) is a diagonal matrix.
(a) Suppose A is invertible. Prove that [A]jj = 0 for all 1 j n.
(Hint: Theorem
Assignment 7Algebra I
Due at the beginning of tutorial Nov. 20
1. This is an alternative proof of Theorem PSPHS in section LC. It says that
in order to nd the solution set to a system of linear equati
Assignment 6Algebra I
Due at the beginning of tutorial Nov 13
1. Suppose v, w Cn .
(a) Suppose a C. Prove
v aw
2
/3
= v , v a v , w a w, v + |a|2 w, w .
(b) Suppose w = 0, and prove that
0 v
by settin
Assignment 1 Algebra I
Due at the beginning of tutorial Sep. 25
1. Suppose F is a eld and b F with b = 0. Prove that the multiplicative
inverse of b is unique. Justify each line in your proof with a e
Assignment 4Algebra I
Due at the beginning of tutorial Oct 23
1. Suppose the RREF of the augmented matrix of a system of linear equations in ve unknowns over C is
/6
1 2 0 0 2
3
0 0 1 0
1
5
0 0 0 1
2