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
1 / 11
1
CH.1 LINEAR EQUATIONS
1.1 Systems of Linear Equations.
1
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 yet
begun to directly affect
graduate business educators
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 Orthogonality and Least Squares
6.1 Inner Product, Leng
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
1 / 11
1
CH.1 MATRIX ALGEBRA
2.1 Matrix Operations.
Dr. Elena Dev
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
1 / 47
1
CH.1 LINEAR EQUATIONS
1.1 Systems of Linear Equations.
1
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
1 / 29
1
CH.1 LINEAR EQUATIONS
1.1 Systems of Linear Equations.
1
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
1 / 18
1
CH.1 LINEAR EQUATIONS
1.1 Systems of Linear Equations.
1
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 corresponding to if it is
non-zero and Av = v .
/6
2. Suppo
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.
(a) Compute the solution set to this system in vector
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 112. Be sure to write the set of vectors.
2. Suppose F is
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 + i)n =
n
2 (cos(n/4) + i sin(n/4)
for all positive inte
Media Literacy Online Project - Serving Educators Around The World
Media Literacy Review
Center for Advanced Technology in Education - College of Education - University of Oregon - Eugene
Mass Media and Cultural Literacy
Bill Walsh, Contributing Writer
E-
Are You Culturally Literate?
Is this what every American needs to know?
Posted May 23, 2011
SHARE
TWEET
SHARE
EMAIL
James Franco GiftedHere is a short test of your cultural literacy. Are you able to place the
following terms in context?
absolute zero (lin
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 been on the faculty since 1984. He received a B.S. in Ma
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:
Survey's Finding of a Drop in Reading Proficiency Is Inexpl
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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 .
(In the lectures we took X = F = R). It turns out that
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 and compute the determinant of
1001
1 2 2 1
A = M44 (Z3
October 10, 2012
1
TEST 1 SOLUTIONSMATH 1102
/10
1. Row-reduce the augmented matrix of the linear system in 3 unknowns
2x2 + 2x3 = 0
3 x1 + 3 x2 + 3 x3 = 3
x1 + x3 = 1
over R into RREF. Indicate every row operation clearly.
Solution: The augmented matrix
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 eld axiom
or a proven theorem.
/5
2. Suppose F is a eld
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 setting a = v , w / w
2
/4
2
| v, w |2
w2
in (a) above.
/3
(c
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 equations, it suces
to have one particular solution and the s
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 NME3)
/4
(b) Suppose [A]jj = 0 for all 1 j n. Prove tha
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 into
RREF. You need not show all row operations, but d
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 (thought
of as row vectors).
(a) Suppose E Mmm (F ) is an
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)
for all positive integers n. (Hint: You may use a lemma p
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 you are
doing.
2. Suppose F is a eld and A Mnn (F ) is a
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 3
0000
0
0
Determine the solution set and then write t