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Spring 2015
Math 461  Linear Algebra for Scientists and Engineers
MATLAB Assignment #3
The rank of a matrix: If A is a matrix, the command rank(A) computes the rank of
A. Because of roundoff errors, it is diffic
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Spring 2015
Prof. Marco Panesi
AE433, Fall 2016
HW #1
Due September 7, 2016 by 5 pm.
Problem 1
Answer the following questions:
(a) What is an airbreathing propulsion system, and what is the difference between ai
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Spring 2015
Math 461 Section P1
Quiz 5 Solution
Feb 28, 2013
2. A salesman has scheduled two appointments to sell encyclopedias. His
first appointment will lead to a sale with probability 0.3, and his second
appo
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Spring 2015
Math 461, Solution to Written Homework 8
1. The joint density function of X and Y is given by
(
24xy, x (0, 1), y (0, 1), 0 < x + y < 1,
f (x, y) =
0,
otherwise .
Are X and Y independent? Find E[X].
S
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Spring 2015
Math 461
Midterm #1  Solution to the practice exam
1. (a)
i. True (definition)
ii. True: The equation A~x = ~b is equivalent to the vector equation x1 a~1 + +xn a~n =
~b.
iii. False: The equation A~x
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Spring 2015
Math 461
Final  Practice exam
This is a practice exam. The actual exam may include material that is not on this practice
exam and the wording of questions may be different. Make sure that you do all
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Spring 2015
Math 461 F
Homework 3 Solutions
Spring 2011
Drew Armstrong
Problems.
p
A.1. How many different (complex) numbers does the expression 1 + 3 represent?
Find a polynomial over Z which has these numbers a
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Spring 2015
Math 461  Linear Algebra for Scientists and Engineers
MATLAB Assignment #4
Eigenvalues and Eigenvectors If A is a square nn matrix, then the command eig(A)
will produce a vector whose entries are the
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Spring 2015
Math 461 C, Spring 2009
Final Exam Solutions and Comments
1. The following parts are independent of each other.
10 pts
(a) What is the coefficient of x9 y 10 z 11 if (x + y + z)30 is expanded? Express
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Spring 2015
Math 461 B/C, Spring 2009
Midterm Exam 2 Solutions and Comments
1. Assume A and B are independent events with P (A) = 0.2 and P (B) = 0.3. Let C denote the event
that none of the events A and B occurs
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Spring 2015
Prof. Daniel J. Bodony
AE433, Fall 2015
AE433Aerospace Propulsion : Fall 2015
Website http:/acoustics.ae.uiuc.edu, click on AE 433 on left.
Instructor Prof. Daniel J. Bodony (AE)
Office
Email
Office
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Spring 2015
Homework 1: Solutions
1. Consider how the de Broglies suggestion might explain some properties of the hydrogen atom.
a. Show that the assumption
h
p = m =
and the quantization condiction that the leng
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Spring 2015
Math 461 Section P1
Quiz 2 Solution
Jan 31, 2013
1. Consider a function f (x1 , x2 , . . . , xn ) of n variables at least r times differentiable. How many different partial derivatives of order r does
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Spring 2015
Math 461 B/C, Spring 2009
Midterm Exam 3 Solutions and Comments
1. Let X have normal distribution with mean 1 and variance 4.
10 pts
(a) Find P (X 1).
Solution.
P (X 1) = P (1 X 1)
X 1
1 1
11
=P
2
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Spring 2015
MATH 461/661 Homework 5
Solutions
1. 3.3.1(a) Let X1 and X2 be the numbers on the two balls drawn, then X = max(X1 , X2 ). The
sample space for the random variables X1 and X2 is S = cfw_1, 2, 3, 4, 5.
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Spring 2015
Math 461 B/C, Spring 2009
Midterm Exam 1 Solutions and Comments
1. Suppose A, B and C are events with P (A) = P (B) = P (C) = 1/3, P (AB) = P (AC) = P (BC) = 1/4
and P (ABC) = 1/5. For each of the fol
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Spring 2015
Math 461 Section P1
Quiz 4 Solution
Feb 13, 2013
1. An urn contains 6 white and 9 black balls. If 4 balls are to be randomly
selected without replacement, what is the probability that the first 2
sele
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Spring 2015
Math 461 Section P1
Quiz 4 Solution
Feb 13, 2013
1. An urn contains 6 white and 9 black balls. If 4 balls are to be randomly
selected without replacement, what is the probability that the first 2
sele
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Spring 2015
Math 461 Section P1
Quiz 6 Solution
March 7, 2013
1. You have $1000, and a certain commodity presently sells for $2 per ounce.
Suppose that after one week the commodity will sell either $1 or $4 per
o
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Spring 2015
ECE474
HOMEWORK #6 SOLUTIONS
SPRING 2012
Problem 6.1 (Problem 10.3 p. 567)
(a) ZB = 1.0
I = 10 A
E = (Z + ZB )I = (0.125 + 1.0)(10) = 11.25 V
Ie
= 0.18 A (from Figure 10.8)
(
)
(
)
200
200
I =
(I +
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Spring 2015
Math 461 Section P1
Quiz 3 Solution
Feb 6, 2013
1. Sixty percent of students at a certain school wear neither a ring nor a
necklace. Twenty percent wear a ring and 30 percent wear a necklace.
If one o
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Spring 2015
Math 461 Section P1
Quiz 9 Solution
April 25, 2013
If X and Y are independent and identically distributed with mean and
variance 2 , find
E[(X Y )2 ].
Solution: We know that
E[Y 2 ] = E[X 2 ] = Var(X)
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Spring 2015
Math 461  Linear Algebra for Scientists and Engineers
MATLAB Assignment #2
More matrix operations:
If A is a matrix with real entries, then A is the transpose of A (if A has complex
entries then A i
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Spring 2015
Math 461
Midterm #2  Solution to the practice exam
1. (a) True or False. Justify carefully your answer.
0
1
i. True: H = span 0 , 1 is a vector space.
0
0
ii. False: ~0 is not in S.
iii. False (t
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Spring 2015
MATH 461/661 Homework 5
Solutions
1. 3.3.1(a) Let X1 and X2 be the numbers on the two balls drawn, then X = max(X1 , X2 ). The
sample space for the random variables X1 and X2 is S = cfw_1, 2, 3, 4, 5.
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Spring 2015
Spring 2013  Math 461
Midterm #2  Solution
1. (a)
(b)
2. (a)
i.
ii.
iii.
iv.
True (such a matrix is invertible).
False (only if ~b = ~0).
True (definition of the kernel of the linear transformation)
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Spring 2015
Math 461
Midterm #2  Practice exam
This is a practice exam. The actual exam may include material that is not on this practice exam and the wording of questions may be different. Make sure that you do
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Spring 2015
Math 461
Practice exam #3  Solution
1. (a) False (the zero matrix is diagonalizable)
(b) False (the identity matrix is diagonalizable but its only evalue is 1)
(c) True (theorem)
(d) True (theorem 
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Spring 2015
Spring 2013  Math 461
Midterm #3  Solutions
1. (a) [10pts]
i.
ii.
iii.
iv.
True (theorem)
False (only if the column of the matrix are linearly independent)
True (theorem)
False (only similar matrice