Name:_
McMaster I.D. #_
McMaster University
Social Sciences 2J03
Dr. Robert Jefferson
Mid Term Examination
Friday, November 4, 2016
Instructions:
1.
On the FRONT of your Scantron (SIDE 1), fill out the items in the box at the top (your
McMaster i.d. numbe
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McMaster University Math1ZC3/1B03 Winter 2013
Page 3 of 16
5.
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MATH 1ZC3/1B03 Day Class: Final Exam - Version 1
Instructors: Bays, Buzano, Lozinski, McLean
Date: April 24, 2013
Duration: 3 hours
Name:
ID #:
Instructions:
This test paper contains 38 multiple choice questions printed on both sides of the page.
The ques
MATH 1ZC3/1B03 Day Class: Final Exam - Version 1
Instructors: Hildum, Lozinski, Tam
Date: April 2014
Duration: 3 hours
Name:
ID #:
Instructions:
This test paper contains 38 multiple choice questions printed on both sides of the page.
The questions are on
MATH 1ZC3/1B03: Test 1 - Version 1
Instructors: Hildum, Lozinski, Tam
Date: February 25, 2014 - Group A
Duration: 90 min.
Name:
ID #:
Instructions:
This test paper contains 23 multiple choice questions printed on both sides of the page.
The questions are
MATH 1ZC3/1B03: Test 1 - Version 1
Instructors: Bays, Buzano, Lozinski, McLean
Date: February 26, 2013 - Group A
Duration: 75 min.
Name:
ID #:
Instructions:
This test paper contains 20 multiple choice questions printed on both sides of the page.
The quest
MATH 1ZCS/1B03: Test 1 - Version 1
Instructors: Bays, Buzano, Lozinski, McLean
Date: February 26, 2013 - Group A
Duration: 75 min.
Name: ID #:
Instructions:
This test paper contains 20 multiple choice questions printed on both sides of the page.
The quest
Elementary matrices
Elementary row operations
The elementary row operations on a matrix are:
Multiply a row by a non-zero constant
Add a constant multiple of one row to another
Interchange two rows
Denition
An elementary matrix is one obtained from an ide
Main facts about elementary matrices
Theorem
If E is an elementary matrix and EA makes sense then if
EA = B, B is the matrix obtained from A by applying the
elementary row operation associated with E.
Corollary
All elementary matrices are invertible.
logo
A fundamental problem
Problem
Given an m n matrix A, nd all the bs such that Ax = b has a
solution.
logo
Bradd Hart
Special matrices
Diagonal matrices
Denition
For a square matrix D = (dij ) is said to be diagonal if dij = 0
whenever i = j.
A diagonal mat
Orthogonality
Denition
We say that two vectors u, v Rn are orthogonal if
u v = 0.
We say that a set of vectors is orthogonal if any two distinct
vectors in the set are orthogonal and the set is
orthonormal if all the vectors have length 1.
logo
Bradd Hart
A quick review
If V is a vector space and X is a subset of V then there is
a subspace W containing X with the property that if any
other subspace W contains X then W W . This
subspace is called the span of X .
The span of X is made up of all linear combin
Vector spaces
Denition
Suppose that V is a non-empty set, + is function on pairs from
V and for every k R and u V , ku is dened. We say that V
together with these operations denes a vector space if the
following axioms are satised for all u, v , w V and k
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1B03/1ZC3 LINEAR ALGEBRA COURSE OUTLINE
Instructor: Dr. Nima Anvari
Email: anvarin@math.mcmaster.ca
Oce Hours: Tuesday and Thursdays 5:00-6:00 HH 407
Course Web Page: Available on Avenue to Learn
Classes: Tuesday and Thursdays 7:00-10:00 pm TSH B105. (Spr
MATH 1ZC3/1B03 - Rough summary of topics covered
Elementary Linear Algebra - Applications Version - 11th Edition - Anton and Rorres
Matlab
Chapter 1: Systems of Linear Equations and Matrices
1.1 Introduction to Systems of Linear Equations - Augmented mat
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