Math 111 2015-16
Assignment 6 Solutions
Due Thursday Jan 21, 2016
1. Find a formula for the nth term of the sequence defined by the third-order recursion
tn+2 = tn+1 + 10tn + 8tn1
with initial values t0 = 1, t1 = 7, t2 = 11. Check that your answer works f
Math 111
Assignment 3 Solutions
Due Thurs October 13 2016
1. The (u, v, y) data points at the right have been observed:
It is desired to fit a regression model of the form
y = u + v.
Find the least squares value of = . Calculate and display
the residu
267
VOL. 85, NO. 4, OCTOBER 2012
Skunk Redux
DAVID KONG
Queens University
Kingston, Ontario, Canada
x.kong@queensu.ca
P E T E R D. T A Y L O R
Queens University
Kingston, Ontario, Canada
peter.taylor@queensu.ca
Peter Taylor opens his linear algebra course
Math 111
Assignment 1 Solution
Due Thursday September 29 2016
There are 5 problems. See the general info on onQ for instructions on how this assignment must be
done and submitted! This assignment is self-assessed. To get full marks (5/5) your work must be
Math 111
Problems for Chapter 1
1
1. Can you write s = 5 as a linear combination of p =
2
1
2. Can you write s = 2 as a linear combination of p =
3
2016 - 2017
1
1 and q =
2
1
1 , q =
0
2
0 ?
4
1
0 and r =
2
2
1 ?
2
3. Write
MATH 111 Complete Notes
Fall 2016
Chapter 3
Transformations
31 Linear transformations
32 Affine transformations
33 Continuous transformations
MATH 111 Chapter 3C 2016-17
1
31C Linear transformations.
Example 311. Below I give you a sequence of basic trans
Math 111
Problems for Chapter 2
2016-17
1.(a) Find a parametric equation for the line passing through the point A = (3, 1, 2) in the direction of the vector
v = [1, 2, 1].
(b) Is the point B = (1, 3, 0) on this line?
2.(a) Find a parametric equation for t
Math 111
Problems for Chapter 3
2016 - 2017
1. Find the matrix of the following linear transformations.
x
x
x y 2z
x y
(b) T x y
y y x
(a) T y
x y
z
(c) A reflection in the plane in the line x = y.
(d) A dilation in the plane along the x-axis
MATH 111 Test 2 Preparation 2014-15
Math 111 Test 2 preparation
Oct 23 2014
Test 2 will be written in class Thursday Oct 30 at 12:30. It will cover the Chapter 2
material. The questions will be technical in nature, that is do you know how to solve
certain
MATH 111 Test 2 Preparation 2015-16
Math 111
Test 2 preparation
Nov 3 2015
Test 2 will be written in class Friday Nov 13. It will cover the Chapter 2 material. The
questions will be technical in nature, that is do you know how to solve certain types of
pr
Fall Review Solutions
1. Find all numbers x for which
(a)
x2 + x + 1 < 0
(b)
1
1
+
>0
x 1 x
(c) |x
1| + |x
(d) |x
2| > 1
1| |x + 2| = 3
Solution.
(a) Since x2 + x + 1 = x + 1 )2 + 3 > 0, the function x2 + x + 1 is always positive.
2
4
1
1
1
(b) The expres
Math 111
Problems for Chapter 2
2015-16
1.(a) Find a parametric equation for the line passing through the point A = (3, 1, 2) in the direction of the vector
v = [1, 2, 1].
(b) Is the point B = (1, 3, 0) on this line?
2.(a) Find a parametric equation for t
Math 111
Test 6 Preparation Problems
March 2016
1. Find the 15th power of z = -1 + i .
z = -1 + i
Write z in polar form
1
- 1 + i = 2 cos(135) + i sin(135)
(-1 + i)15 = ( 2 )15cos(15 135) + i sin(15 135)
To simplify this, note that 8135 is a multiple of 3
Math 111
Problems for Chapter 5
2015 - 2016
1. Consider the "win or lose" game with the transition matrix at the
right.
(a) Suppose you have a choice whether to start on node X or node Y.
Which should you choose to maximize your probability of winning?
(b
page 1
MATH 111 Complete Notes
Winter 2016
Chapter 5
Games and State Transitions
6
5
4
1
2
3
50 Series
51 Board Games
52 Reproduction
53 Complex Numbers
54 Complex Systems
MATH 111 Chapter 5C 2015-16
1
page 2
50C Series
Series: general concepts
An infinit
Math 111
Assignment 2 Solutions
Due Thursday October 6 2016
There are 6 problems. See the general info on OnQ for instructions on how this assignment
must be done and submitted! This assignment is self-assessed. To get full marks (5/5) your
work must be w
Appendix
Skunk redux
This is a simplified version of the game "skunk" that is popular in elementary school math classrooms. The original game is hard to "solve"
completely, but this version provides an excellent elementary problem.
Here's how the game is
Math 111
Assignment 1 Solutions
Due Thursday Sept. 26 2013
1. Consider the system: Au = k where A = [p q r]:
1 2 r u
2 1 4 v =
1 1 1 w
3
k .
2
In terms of the two unknown parameters r and k, how many solutions [u, v, w] does the system
have? This
Math 111
Assignment 3 Solutions
Due Thursday Oct 24, 2013
1. The (u, v, y) data points at the right have been observed:
It is desired to fit a regression model of the form
y = u + v.
Find the least squares value of = . Calculate and display
the residu
Math 111
Assignment 10 Solutions
Due Thursday April 3rd 2014
1. Find the nine 9th roots of 512i. Those that can be expressed simply in terms of a square root
should be rewritten that way. Display these roots on a complex plane diagram.
Solution.
Since 512
Page 1 of 4 pages
MATH 111 Test 5 Solutions March 3 2014
_
NAME: LAST
FIRST
Math 111
_
Student #
Test 5 Solutions
Feb 3 2014
There are 4 questions on 4 pages. The first three are worth 6 marks each and the last two
are worth 3 marks each.
1 2 3 4
5
6
n
Math 111 2013-14
Assignment 5 Solutions
Due Thursday Nov. 28, 2013
1. Decompose the transformation pictured below as
(a) a rotation about the origin followed by a translation
(b) a translation followed by a rotation about the origin
(c) a rotation about a
Page 1 of 4 pages
MATH 111 Test 3 Solutions Nov. 21 2013
_
NAME: LAST
FIRST
Math 111
_
Student #
Test 3 Solutions
Nov 21 2013
There are 4 questions on 4 pages worth 6 marks each. Work carefully. Answer in
the space provided. If you need extra space advise
Math 111
Test 6 Solutions
March 31 2014
1. A complex number z has modulus r = 10 and argument = 100. For both parts below give an exact
answer and a 2-place decimal approximation
(a) Calculate the real part of z4.
(b) Calculate the imaginary part of one o
Math 111 2013-14
Assignment 2 Solutions
Due Thursday Oct. 10.
Note: Many of you made errors in your work so got the wrong answer. Please note that there is a
simple way to check the correctness of the answer for most of these problems. In such cases
there
Math 111
Assignment 9 Solutions
1. Consider a population in which individuals progress through three
stages: juvenile X, subadult Y and adult Z. Suppose that each year
juveniles survive with probability p and become subadults, subadults
survive with proba
Math 111 2013-14
Assignment 8 Solutions
Due ThursdayMarch 6, 2014
1. By calculating the first few cases, find a simple expression for the sum:
Sn = 11! + 22! + 33! + nn! .
[Hint: they grow like factorials so calculate the quantities 1!, 2!, 3!, 4!, 5!, 6!
Page 1 of 4 pages
MATH 111 Test 4 Solutions Feb 3 2014
_
NAME: LAST
Math 111
FIRST
_
Student #
Test 4 Solutions
Feb 3 2014
There are 4 questions on 4 pages. The first three are worth 6 marks each and the last is
worth 3 marks. Work carefully. Answer in th
Math 111 2013-14
Assignment 6 Solutions
Due Thursday Jan 23, 2014
1. Find a formula for the nth term of the sequence defined by the third-order recursion
tn+2 = 3tn+1 + 6tn 8tn1
with initial values t0 = 3, t1 = t2 = 6 . Check that your answer works for t3