University of Ottawa
Department of Mathematics and Statistics Math 1302A: Mathematical Methods II Instructor: Alistair Savage Final Exam April 15, 2008 Solutions
Surname Student #
First Name
Instructions: (1) You have 180 minutes to complete this exam. (2
MAT 1302 - Mathematical Methods II
Alistair Savage
Mathematics and Statistics
University of Ottawa
Winter 2010 Lecture 18
Alistair Savage (uOttawa)
MAT 1302 - Mathematical Methods II
Winter 2010 Lecture 18
1 / 30
Announcements
Third Assignment
Solutions n
University of Ottawa
Department of Mathematics and Statistics
MAT 1302: Mathematical Methods II
Instructor: Alistair Savage
Final Exam
23 April 2012
Surname
First Name
Student #
Instructions:
(a) You have 3 hours to complete this exam.
(b) This exam consi
University of Ottawa
Department of Mathematics and Statistics
Math 1302A: Mathematical Methods II
Instructor: Alistair Savage
Final Exam April 15, 2008
Surname
First Name
Student #
Instructions:
(1) You have 180 minutes to complete this exam.
(2) This exa
University of Ottawa
Department of Mathematics and Statistics
MAT 1302A: Mathematical Methods II
Instructor: Alistair Savage
Third Midterm Test Solutions White Version
26 March 2013
Surname
First Name
Student #
DGD (14)
Instructions:
(a) You have 80 minut
University of Ottawa
Department of Mathematics and Statistics
MAT 1302A: Mathematical Methods II
Professor: Aziz Khanchi
Final Exam Solutions
April 2010
Surname
First Name
Student #
Seat #
Instructions:
(a) You have 3 hours to complete this exam.
(b) This
University of Ottawa
Department of Mathematics and Statistics
MAT 1302: Mathematical Methods II
Instructor: Alistair Savage
Final Exam
23 April 2012
Surname
First Name
Student #
Instructions:
(a) You have 3 hours to complete this exam.
(b) This exam consi
1
1.
Find all k for which the following system has infinitely many solutions.
x + 2y +
z=0
x + 3y + 2kz = 0
2x + 3y + kz = 0
A.
B.
C.
D.
E.
F.
0
1/2
3
-3
1
-1
2.
The coefficient matrix A in a homogeneous system of 12 equations in 16 unknowns
is known to h
MAT 1302 D FINAL EXAM April, 12th 2011
Instructor: Termeh Kousha
NAME
I.D.#
Duration: 3 hours
NO CALCULATORS. NO BOOKS. NO NOTES.
Instructions: This exam consists of 10 multiple choice questions and 8 Long answer questions on 16 pages. The marks for each
University of Ottawa
Department of Mathematics and Statistics
MAT 1302A: Mathematical Methods II
Instructor: Alistair Savage
Final Exam
April 2013
Surname
First Name
Student #
Seat #
Instructions:
(a) You have 3 hours to complete this exam.
(b) This exam
Mathematical Methods II
MAT 1302B Winter 2016
Instructor: Roberto Pirisi, Room 302, home page
http:/science.uottawa.ca/mathstat/en/people/pirisi-roberto
Prerequisites: One of Ontario 4U Mathematics of Data Management (MDM 4U), Ontario 4U
Advanced Function
MAT1302F Mathematical Methods II
Lecture 3
Aaron Christie
20 January 2015
1
Types of Solution Sets
Last time we gave the definitions of the row echelon and reduced row echelon forms of a matrix (REF and RREF, respectively). Then we described
Gauss-Jordan
MAT 1302A Mathematical Methods II
Alistair Savage
Mathematics and Statistics
University of Ottawa
Winter 2014 Lecture 6
Alistair Savage (uOttawa)
MAT 1302A Mathematical Methods II
Winter 2014 Lecture 6
1 / 31
Announcements
First Midterm:
Second class of n
MAT 1302A Mathematical Methods II
Rostislav Devyatov
Mathematics and Statistics
University of Ottawa
Winter 2017 Lecture 6
Vector parametric form of general solution, homogeneous systems of
linear equations, recall
Textbook sections: LC.VFSS, HSE
Rostisla
LING2001 Homework 1
Due by class on Monday, February 3rd
65 points total
1. Transcribe your full name (first and last) using IPA. (3 points)
2. Provide one minimal pair (two words that differ only by the specified speech sounds) for each of the following
MAT 1302A Mathematical Methods II
Rostislav Devyatov
Mathematics and Statistics
University of Ottawa
Winter 2017 Lecture 5
Matrix-vector multiplication, application: network flow
Textbook sections: MM.MVP, SS.SSV
Rostislav Devyatov (uOttawa)
MAT 1302A Mat
MAT 1302A Mathematical Methods II
Rostislav Devyatov
Mathematics and Statistics
University of Ottawa
Winter 2017 Lecture 3
Solving systems of linear equations: general solution, examples,
properties of echelon forms and of row reduction, coefficient matri
MAT 1302A Mathematical Methods II
Rostislav Devyatov
Mathematics and Statistics
University of Ottawa
Winter 2017 Lecture 2
Solving systems of linear equations: reduced echelon form, row
reduction algorithm, general solution
Rostislav Devyatov (uOttawa)
MA
MAT 1302A Mathematical Methods II
Rostislav Devyatov
Mathematics and Statistics
University of Ottawa
Winter 2017 Lecture
Coefficient matrix of SLE, vectors, vector operations, linear
combinations, span
Textbook sections: SSLE.MVNSE, VO, LC, SS.SSV
Rostisl
University of Ottawa
Department of Mathematics and Statistics
MAT 1302C : Mathematical Methods II
Professor: Hadi Salmasian
First Midterm Exam Version A
October 11, 2012
Surname
First Name
Student #
DGD (Tuesday/Thursday)
Instructions:
(a) You have 80 min
1. Solve the system of linear equations:
3x1 + 6x2 = 3
5x1 + 7x2 = 10
2. Find the point of intersection of the lines x1 + 2x2 = 13 and 3x1 2x2 = 1.
3. Solve the system of linear equations:
x1 5x2 + 4x3 = 3
2x1 7x2 + 3x3 = 2
2x1 + x2 + 7x3 = 1
4. Solve the
1. Do the three planes 2x1 + 4x2 + 4x3 = 4, x2 2x3 = 2, and 2x1 + 3x2 = 0 have at least
one common point of intersection? Explain.
2. Determine the value(s) of h such that the matrix is the augmented matrix of a consistent
linear system.
1 h 5
2 8 6
3. De
1. Suppose that the matrix of an SLE has the following form, where denotes an arbitrary
entry, 0 denotes a zero entry, and denotes a nonzero entry. How many solutions does the
system have?
(a)
0
0 0
(b)
0 0
0 0 0
2. Determine the value(s) of h s
MAT1302F Mathematical Methods II
Lecture 4
Aaron Christie
22 January 2015
Last class we completed the first stage of the course, which concerned
using some linear algebraic tools to solve systems of linear equations. The
main result was that it is always
MAT1302F Mathematical Methods II
Lecture 17
Aaron Christie
24 March 2015
1
Eigenvalues and Eigenvectors
Today were going to start looking at a topic that on the surface might seem
like a mere curiousity but turns out to be of major importance in linear
a
MAT1302B Mathematical Methods II
Lecture 2
Aaron Christie
15 January 2015
1
Echelon Forms
Last class introduced the objects that will motivate our study of linear algebra for the first few classes. Specifically, we saw definitions of linear equations, li
MAT1302F Mathematical Methods II
Lecture 12
Aaron Christie
3 March 2015
1
Vector Subspaces
This class, were going to back away from solving specific problems and start
building on the theory of vector spaces. In particular, were going to study
substructu
MAT1302F Mathematical Methods II
Lecture 10
Aaron Christie
24 February 2015
The big news last lecture was the introduction of matrix inverses, which,
for certain square matrices, give us a way to approach solving matrix equations in somewhat the same way
University of Ottawa
Department of Mathematics and Statistics
MAT 1302B: Mathematical Methods II
Instructor: Alistair Savage
Final Exam Solutions
April 2015
Surname
First Name
Student #
Seat #
Instructions:
(a) You have 3 hours to complete this exam.
(b)
MAT1302F Mathematical Methods II
Lecture 20
Aaron Christie
7 April 2015
1
Difference Equations & Markov Chains: Modelling Systems Over Time
This will be the last lecture of new material, and well spend it looking at
how we can use the topics covered in t
MAT1302F Mathematical Methods II
Lecture 7
Aaron Christie
3 February 2015
1
Linear Dependence and Independence
Last class we studied homogeneous systems how their solutions are related
to the general solutions of arbitrary linear systems and how to write
MAT1302F Mathematical Methods II
Lecture 15
Aaron Christie
17 March 2015
1
Determinants. More Determinants.
1.1
A Quick Recap
Last class we picked up a loose thread from back when matrix inverses were
first introduced and gave the definition of a determi
MAT1302F Mathematical Methods II
Lecture 19
Aaron Christie
2 April 2015
1
Eigenvectors, Eigenvalues, and Diagonalization
Now that the basic theory of eigenvalues and eigenvectors is in placemost
importantly a procedure that allows us to find all the eige