HOMEWORK 5
511 LINEAR ALGEBRA WITH APPLICATIONS
FALL 2016
From the official course book - Linear Algebra and its applications (Gilbert
and Strang, fourth edition):
Section 2.2
pag 85 ex. 12, 19, 24, 25, 26, 63.
Section 2.3
pag 98 ex. 6, 27, 35, 40.
The ho
HOMEWORK 5
511 LINEAR ALGEBRA WITH APPLICATIONS
FALL 2015
From the official course book - Linear Algebra and its applications (Gilbert
Strang):
Section 2.6.
pag 149 156
ex. 2, 3, 5, 7, 19, 50
Chapter 2. Review Excercises
pag 154 158
ex. 1.11, 1.13, 1.22,
MA 511
REVIEW FINAL
1. Which of the following sets of vectors are linearly independent?
i) (0, 0, ), (0, 1, 1), (0, 2, 3)
ii) (1, 2, 3), (4, 5, 6), (7, 8, 9)
iii) (1, 0, 0), (0, 0, 0), (0, 0, 1).
A. i)
B. ii)
C. iii)
D. i) and iii)
2. Find the inverse of
FINAL EXAM
MA 511
Fall 2007
Name:
Student Number:
Do not use notes, books, or calculators. Work individually
Part I
Answer each of the following as True or False. 4 pts. each.
1. Given an m n matrix A, the equation Ax = 0 has only a trivial
solution if it
Sample Problems
MA 511
Part I
Answer each of the following as True or False.
1. If A and B are Hermitian matrices with the same eigenvalues then
there is a unitary U such that U BU H = A.
2. If A is a square matrix such that the linear transformation f (x
MIDTERM EXAM II
MA 511
Spring 2003
Name:
Student Number:
Do not use notes, books, or calculators. Work individually
Part I
Answer each of the following as True or False. 2 pts. each.
1. All Fourier matrices are Hermitian.
2. The dierential equation du/dt
MIDTERM EXAM II
MA 511
Spring 2004
Name:
Student Number:
Do not use notes, books, or calculators. Work individually
Part I
Answer each of the following as True or False. 2 pts. each.
1. All Fourier matrices are unitary.
2. The dierential equation du/dt =
MIDTERM EXAM II
MA 511
Spring 2007
Name:
Student Number:
Do not use notes, books, or calculators. Work individually
Part I
Answer each of the following as True or False. 2 pts. each.
2
1. If Fn is a Fourier matrix then Fn = nI.
2. The dierential equation
Sample Problems 2.
MA 511
Fall 2005
1. Answer each of the following as True or False.
(a) If P 2 = P and P = P T then P is a projection matrix.
(b) If P is a projection matrix and P is invertible then P = I.
(c) The row space of a square matrix is orthogo
MIDTERM EXAM II
MA 511
Spring 2008
Name:
Student Number:
Do not use notes, books, or calculators. Work individually
Part I
Answer each of the following as True or False. 3 pts. each.
1. If det(A) = 2 and det(B) = 4 are 3 3 matrices then det(2A)1 B 3 ) =
1
Sample Problems for MIDTERM EXAM I
Part I
1. If A and B are nonsingular then AB = BA.
2. If A is an m n and B is n r matrix then N (AB) N (A).
3. If A is symmetric then RART is symmetric.
4. If u1 and u2 are solutions to the nonhomogeneous system Ax = b,
MIDTERM EXAM I
MA 511
Spring 2007
Name:
Student Number:
Do not use notes, books, or calculators. Work individually
Part I
Answer each of the following as True or False. 3 pts. each.
1. If A and B are nonsingular then AB = BA.
2. If A is an m n and B is n
HOMEWORK 7
511 LINEAR ALGEBRA WITH APPLICATIONS
FALL 2015
From the official course book - Linear Algebra and its applications (Gilbert
Strang):
Section 3.3.
pag 190 195
ex. 19, 21, 30, 40, 41
Section 3.4.
pag 208 211
ex. 8, 13, 15, 23, 24, 32
The homework
HOMEWORK 10
511 LINEAR ALGEBRA WITH APPLICATIONS
FALL 2015
From the official course book - Linear Algebra and its applications (Gilbert
Strang):
Section 4.4.
pag 253 259
ex. 20, 25, 30, 41, 43
Section 5.1.
pag 268 272
ex. 5, 8, 14, 20, 24, 27, 29, 38
Sect
HOMEWORK 3
511 LINEAR ALGEBRA WITH APPLICATIONS
FALL 2015
From the official course book - Linear Algebra and its applications (Gilbert
Strang):
Section 2.1.
pag 73 - 77
ex. 8, 11, 12
Section 2.2.
pag 85 - 91
ex. 9, 13, 24, 25, 43
Section 2.3.
pag 98 - 102
9/14/2015 LDL factorization of symmetric matrices and Cholesky factorization of Positive denite matrices
Next: Permutation Matrix Up: Direct Methods for Linear Previous: Doolittle Crout's and Choleski
LDL factorization of symmetric matrices and Cholesky
HOMEWORK 1
511 LINEAR ALGEBRA WITH APPLICATIONS
FALL 2015
From the official course book - Linear Algebra and its applications (Gilbert
Strang):
Section 1.2
pag 10 ex. 1, 3, 10.
Section 1.3
pag 17 ex. 11, 15, 24.
Section 1.4.
pag 30 ex. 10, 11, 13.
Section
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Midterm Math 511 (Moh) Sept 30 2015
6 Write your answers on the test paper!
a For decimal approximations, it is enough to give 2 decimal places.
0 Show enough of your work that your reasoning can be followed.
0 There are 6 p
HOMEWORK 8
511 LINEAR ALGEBRA WITH APPLICATIONS
FALL 2015
From the official course book - Linear Algebra and its applications (Gilbert
Strang):
Review Exercises Chapter 3.
pag 221 224
ex. 3.31, 3.33, 3.36, 3.38
Section 4.2.
pag 231 236
ex. 7, 12, 14, 20,
HOMEWORK 9
511 LINEAR ALGEBRA WITH APPLICATIONS
FALL 2015
From the official course book - Linear Algebra and its applications (Gilbert
Strang):
Section 4.3.
pag 241 247
ex. 1, 4, 5, 7, 13, 17, 27, 30, 40, 43
Section 4.4.
pag 253 259
ex. 2, 4
The homework
HOMEWORK 6
511 LINEAR ALGEBRA WITH APPLICATIONS
FALL 2016
From the official course book - Linear Algebra and its applications (Gilbert
and Strang, fourth edition):
Section 2.3
pag 98 ex. 13, 16, 20, 29, 30.
Section 2.4
pag 110 ex. 4, 6, 9, 18, 29, 37
The
HOMEWORK 2
511 LINEAR ALGEBRA WITH APPLICATIONS
FALL 2015
From the official course book - Linear Algebra and its applications (Gilbert
Strang):
Chapter 1. Review Excercises
pag 65 - 67
ex. 1.12, 1.13, 1.15, 1.17, 1.27, 1.28.
The homework is due on Tuesday
HOMEWORK 6
511 LINEAR ALGEBRA WITH APPLICATIONS
FALL 2015
From the official course book - Linear Algebra and its applications (Gilbert
Strang):
Section 3.1.
pag 167 171
ex. 11, 28, 33, 38.
Section 3.2.
pag 177 180
ex. 3, 8, 14, 22, 25.
Section 3.3.
pag 19
Practice Problem Set 21
MATH 511
1. Let V be the row space of
Spring 2015
1 2 3
A = 4 5 6 .
7 8 9
Also, let W be the column space of
1 1
B = 0 1 .
2 4
(1) Find V , V + W .
(2) Which of the following statements is true?
A.
B.
C.
D.
E.
V and W are orthogona
HOMEWORK 11
511 LINEAR ALGEBRA WITH APPLICATIONS
FALL 2015
From the official course book - Linear Algebra and its applications (Gilbert
Strang):
Section 5.5
pag 321 326
ex. 8, 9, 11, 12, 14, 15, 19, 30
Section 5.6.
pag 335 340
ex. 1, 11, 16, 30
The homewo
Solutions and comments, first exam, fall 2006.
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1. Find all solutions of the equation z 3 = 8i. The answer should be given in
an algebraic form, that is using arithmetic operations and radical
Math 511, Spring 2012 Midterm exam solutions
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1. Circle the letters corresponding to the statements which are true for all
m n matrices A and B, where m < n:
A. Ax = 0 has infinitely many solu
MA 511 EXAM 1 Fall 2001
SOLUTIONS
1) (a) Given that the last two rows of A are linear combinations of the rst two, nd the
LU factorization of
1 2 0 1
1 2 1 1
A z
a b c d
e f g h
SOLUTION: Note that the linear combinations of the rst two rows are c(1 2 0 1
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https:/www.coursehero.com/file/8539482/Quiz-2-Solution/
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https:/www.coursehero.com/file/8539482/Quiz-2-Solution/
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