Assignment 1 for Math 208 [A01], 2012
Due Day: Thursday, January 26, 2012 at the class, late assignments will
not be accepted
There are ten problems for you to solve and hand in. Illegible, disorganized or missing
solutions will receive no credit. Please
MATHEMATICS 208 [A01]
Test 1-version 1 (Monday, September 29, 2014)
Dr. Jane Ye
Name:
Student Number:
No notes, books, or rough paper please. Show all your work neatly, part marks may be
awarded. The only calculator that may be used for the test is the st
MATHEMATICS 208 [A01]
Solutions to Test 1, version 1 (Monday, January 25, 2016)
Dr. Jane Ye
Name:
Student Number:
No notes, books, or rough paper please. The only calculator that may be used for the
test is the standard calculator Sharp EL-510R or Sharp E
MATHEMATICS 208 [A01]
Solutions to Test 2-version 1 (Monday, February 29, 2016)
Dr. Jane Ye
Name:
Student Number:
No notes, books, or rough paper please. The only calculator that may be used for the
test is the standard calculator Sharp EL-510R or Sharp E
MATHEMATICS 208 [A01]
Solutions to Test 3-version 1 (MONDAY, MARCH 21, 2016)
Dr. Jane Ye Name:
Student Number:
No notes, books, or rough paper please. The only calculator that may be used for the
test is the standard calculator Sharp EL-510R or Sharp EL—S
Solutions to Extra problems for Test 1, Math 208
Please note that this is not a sample midterm. They are just extra questions. In your review,
please also go over all the homework questions assigned.
1. Write A = [aij ] if A is 2 3 and aij = 2i j.
Solutio
Solutions for Extra problems for Test 2, Math 208
Please note that these questions are extra. In your review, please also go over all the homework
questions assigned. Try to solve the following problems on your own and check the solutions if you
need to.
Solutions for Extra problems for Test 3, Math 208
1. Write the quadratic form for each of the following symmetric matrix
2 —1 —3 4 —3 4 2 4
(a)(~11) (b)(4 —5) (C)(4 —6) (d)(48)
—4 0 0
(e) 0 —l 2
0 2 ~41
and determine if the quadratic form is strictly conv
Lecture Notes on Multivariate Calculus and Optimization
by Jane Ye
Notations:
A set is any collection of items. For example R is the set of all real numbers.
x R means x is in the set R.
R+ = cfw_x R : x 0 is the set of all nonnegative numbers.
R+ = c
Notes for Math 208: Linear Algebra: Part II
Part 6: Inverse of a matrix
Let A = (aij )nn be a square matrix of size n. If there exists a matrix C such
that CA = AC = In where In is the identity matrix of size n, then C is called the
inverse matrix of A an
MATHEMATICS 208 [A01]
Solutions to Test 2 (Monday, February 29, 2016)
Dr. Jane Ye
Name:
Student Number:
No notes, books, or rough paper please. The only calculator that may be used for the
test is the standard calculator Sharp EL-510R or Sharp EL-510RNB.
MATHEMATICS 208 [A01]
Solutions to Test 1 (Monday, January 25, 2016)
Dr. Jane Ye
Name:
Student Number:
No notes, books, or rough paper please. The only calculator that may be used for the
test is the standard calculator Sharp EL-510R or Sharp EL-510RNB. Y
Solutions for Extra problems for Test 2, Math 208
Please note that these questions are extra. In your review, please also go over all the homework
questions assigned. Try to solve the following problems on your own and check the solutions if you
need to.
Notes for Math 208: Linear Algebra: Part I
Part 1: Systems of linear equations
Consider a system of m linear equations with n variables:
a11 x1 + a12 x2 + + a1n xn = b1
a21 x1 + a22 x2 + + a2n xn = b2
am1 x1 + am2 x2 + + amn xn = bm .
It is homogeneous if
MATHEMATICS 208 [A01]
Test 3 (Thursday, November 20, 2014)
Dr. Jane Ye
Name:
Student Number:
No notes, books, or rough paper please. The only calculator that may be used for the
test is the standard calculator Sharp EL-510R or Sharp EL-510RNB. You must si
Extra problems for Test 1, Math 208, 2014
Please note that this is not a sample midterm. They are just extra questions. In
your review, please also go over all the homework questions assigned. Please nish
the regular homework before trying these problems.
Extra problems for Test 1, Math 208, 2014
Please note that this is not a sample midterm. They are just extra questions. In
your review, please also go over all the homework questions assigned.
1. Write A = [aij ] if A is 2 3 and aij = 2i j.
2. Sove the ma
Extra problems for Test 2, Math 208
Please note that these questions are extra. In your review, please also go over all
the homework questions assigned. Try to solve the following problems on your own
and check the solutions if you need to.
1. For the fol
Solutions for Extra problems for Test 3, Math 208
1. Determine the deniteness of the following symmetric matrices by using the
test in terms of eigenvalues.
(a)
1
2
1
4
(e)
1
(b)
0
0
4
5
(c)
3
4
3
4
4
6
(d)
2 4
4 8
0
1
2
0
2
4
Solution. (a) The chara
Extra problems for Test 3, Math 208
1. Determine the deniteness of the following symmetric matrices by using the
test in terms of eigenvalues.
2
1
1
1
(b)
4
0
(a)
(e) 0
1
0
2
0
3
4
4
5
(c)
3
4
4
6
(d)
2 4
4 8
2
4
2. Write the quadratic form for each
Lecture Notes on Optimization, Part I
by Jane Ye
Notations:
A set is any collection of items. For example R is the set of all real numbers.
x R means x is in the set R.
R+ = cfw_x R : x 0 is the set of all nonnegative numbers.
R+ = cfw_x R : x > 0 is
Lecture Notes on Optimization: Part II
by Jane Ye
Quadratic Forms:
Given an n n matrix A and a n 1 vector x, the scalar-valued function
q(x) = x Ax
is a quadratic form. There is no loss of generality in assuming that the matrix which
generates the form i
Notes for Math 208: Linear Algebra
Part 1: Systems of linear equations
Consider a system of m linear equations with n variables:
a11 x1 + a12 x2 + + a1n xn = b1
a21 x1 + a22 x2 + + a2n xn = b2
am1 x1 + am2 x2 + + amn xn = bm .
It is homogeneous if all b1
MATHEMATICS 208 [A01]
Solutions to Test 1 (Tuesday, October 6, 2015)
Dr. Jane Ye
Name:
Student Number:
No notes, books, or rough paper please. The only calculator that may be used for the
test is the standard calculator Sharp EL-510R or Sharp EL-510RNB. Y
MATHEMATICS 208 [A01]
Solutions to Test 3 (MONDAY, MARCH 21, 2016)
Dr. Jane Ye Name:
Student Number:
No notes, books, or rough paper please. The only calculator that may be used for the
test is the standard calculator Sharp EL-510R or Sharp EL—SIORNB. You
Answers to even number questions and supplementary exercises for Math 208
2.3 #2. C is unbounded and convex. Interpretation of x and x0 : the minimal consumption
that is necessary for the further existence of the consumer.
#8. X = [1, 2] [3, 4]. Take x1
Supplementary Excecises for Math 208 (Subject to revision)
Ch. 7
1. Solve the linear systems given in 7.2#1(a) by row reduction.
2. Find the solutions in parametric form for the linear systems given in 7.2#1(b)(e).
Ch. 10
3. Are the rows linearly independ
Lecture Notes on Multivariate Calculus and Optimization
by Jane Ye
Notations:
A set is any collection of items. For example R is the set of all real numbers.
x R means x is in the set R.
R+ = cfw_x R : x 0 is the set of all nonnegative numbers.
R+ = c
Notes for Math 208: Linear Algebra: Part I
Part 1: Systems of linear equations
Consider a system of m linear equations with n variables:
a11 x1 + a12 x2 + + a1n xn = b1
a21 x1 + a22 x2 + + a2n xn = b2
am1 x1 + am2 x2 + + amn xn = bm .
It is homogeneous if
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