MAT223 Theorems
Section 1.2 Row Reduction and Echelon Form:
T H E O R E M 2 Existence and Uniqueness Theorem
A linear system is consistent if and only if the rightmost column of the augmented matrix is not
a pivot columnthat is, if and only if an echelon
UNIVERSITY OF TORONTO MISSISSAUGA
I DECEMBER 2015 FINAL EXAMINATION
MAT223H5F - Linear Algebra I
M. Lukic, A. Rennet, J. Thind, J. Yang
Duration: 3 hours
Aids: None
NAME (PRINT):
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STUDENT #: SIGNATURE:
The University
MAT 223 - ASSIGNMENT # 1
DUE WEEK OF JANUARY 9
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TUTORIAL:
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Problem
Points
Grade
2
2
2
P Total
1
7
Instructions
Please submit solutions to the textbook questions listed below. Your assignment is due
MAT 223 - ASSIGNMENT # 2
DUE WEEK OF JANUARY 30
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Problem
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2
2
2
P Total
1
7
Instructions
Please submit solutions to the textbook questions listed below. Your assignment is due
MAT 223 - ASSIGNMENT # 2
DUE WEEK OF JANUARY 16
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Problem
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2
2
2
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1
7
Instructions
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MAT 223 - ASSIGNMENT # 4
DUE WEEK OF OCTOBER 17
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Problem
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2
2
2
P Total
1
7
Instructions
Please submit solutions to the textbook questions listed below. Your assignment is due
MAT 223 - ASSIGNMENT # 2
DUE WEEK OF SEPTEMBER 19
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2
2
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1
7
Instructions
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MAT 223 - PRACTICE PROBLEMS
Instructions: These are NOT to be handed in. But, you are expected to work on these problems
regularly, in order to keep up with the course, and be adequately prepared for quizzes, tests and
exams. Throughout the semester I wil
MAT 223 - ASSIGNMENT # 6
DUE WEEK OF NOVEMBER 7
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Problem
Points
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2
2
2
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1
7
Instructions
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MAT 223 - ASSIGNMENT # 7
DUE WEEK OF NOVEMBER 14
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Problem
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Grade
2
2
2
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1
7
Instructions
Please submit solutions to the textbook questions listed below. Your assignment is du
MAT 223 - ASSIGNMENT # 5
DUE WEEK OF OCTOBER 24
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2
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7
Instructions
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Lecture 2 - Supplementary Notes
Definition. A matrix is said to be in row-echelon form if
1) All zero rows are at the bottom.
2) The first non-zero entry from the left in each row is 1 (called a leading 1).
3) Each leading 1 is to the right of all leading
Lecture 3
John Yang
UTM
September 13, 2016
John Yang
Lecture 3
Vectors
Definition
An n-vector v is an ordered set of n numbers. It can be
represented as:
a) an n-tuple: v = (a1 , a2 , . . . , an ),
b) an 1 n matrix (a row vector): v = a1 a2 . . .
a1
a2
MAT 223F - EXAM REVIEW SHEET
PAGE 1
OF
4
The time and location of the exam can be found by clicking here. Please show up 5-10 minutes
early to get seated, as the exam will start on time; with or without you!
Please note that exams start on the hour, not
Topics and Practice Problems for Test 2
1. Section 1.9: The matrix of linear transformation:
(1) If T : Rn 7 Rm is a linear transformation, then T (x) = Ax where
A = [T (e1 ) T (e2 ) . . . T (en )]
and e1 , . . . , en are columns of the identity matrix of
Linear Algebra Midterm 1 Review
Definitions and Concepts (you should be able to state/apply the denition/concept):
Elementary row operations:
1. (Replacement) Replace one row by itself plus a multiple of another.
2. (Interchange) Interchange two rows.
3.
University of Toronto Mississauga
Instructors: M. Tvalavadze
Departement of Mathematics
K . Shaw
Linear Algebra I - MAT223
Test 1 - October 10, 2012
Last name:
First name:
Student number:
You have 50 minutes to complete the test.
No calculators, books or
University of Toronto Mississauga
Instructors: M. Tvalavadze
Departement of Mathematics
K . Shaw
Linear Algebra I - MAT223
Test 2 - November 7, 2012
Last name:
First name:
Student number:
Section:
Tutorial section:
You have 50 minutes to complete the test
MAT 223 - ASSIGNMENT # 1
DUE WEEK OF SEPTEMBER 12
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2
2
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1
7
Instructions
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MAT 223 - ASSIGNMENT # 3
DUE WEEK OF OCTOBER 3
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7
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MAT 223 - ASSIGNMENT # 7
DUE WEEK OF NOVEMBER 23
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2
2
2
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2
10
Instructions
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MAT 223 - ASSIGNMENT # 3
DUE WEEK OF OCTOBER 12
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2
2
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2
10
Instructions
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For students in a M
MAT 223 - ASSIGNMENT # 5
DUE WEEK OF NOVEMBER 2
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10
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MAT 223 - ASSIGNMENT # 6
DUE WEEK OF NOVEMBER 9
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2
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2
10
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MAT 223 - ASSIGNMENT # 1
DUE WEEK OF SEPTEMBER 14
NAME (PRINT):
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Grade
2
2
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2
10
Instructions
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MAT 223 - ASSIGNMENT # 1
DUE WEEK OF SEPTEMBER 28
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2
2
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2
10
Instructions
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MAT 223 - ASSIGNMENT # 4
DUE WEEK OF OCTOBER 19
NAME (PRINT):
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Problem
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Grade
2
2
2
2
P Total
2
10
Instructions
Please submit solutions to the textbook questions listed below. Your assignment is