Sophie Chrysostomou
Digitally signed by Sophie Chrysostomou DN: cn=Sophie Chrysostomou, o=UTSC, ou=Division of Computer and Mathematical Sciences, email=chrysostomou@utsc. utoronto.ca, c=CA Date: 2008.01.08 14:52:14 -05'00'
University of Toronto at Scarbo
University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
Linear algebra I
MATA23 Winter 2016
Fraleigh & Beauregard, Pages 68 71
1
40.
2
3
University of Toronto
Christopher Shim 2016
University of Toronto at Scarborough
University of Toronto
Department of Computer & Mathematical Science MATA23: Linear
Algebra Final Review
1. Vectors
(1) Formulas
Parallel Vectors: None
zero vectors
and
are
v
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
FINAL EXAMINATION
MATA23H3 - Linear Algebra I
Examiner: E. Moore
K. Smith
Date: April 17, 2014
Duration: 3 hours
1. [10 points]
(a)
i. Define what it means for a subset W of
MATA23
Solution 6
Solution 6
1) to 3) Read the lectures and the book to answer them.
4) Section 2.3
MATA23
Solution 6
T is one to one and onto
For 23) T is one to one and onto,
University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MAT A23S
Winter 2012
Term Test Info
Time:
Friday March 9th 7:00 PM - 9:00 PM
Location:
You write in the room:
SW128:
SW143
SW309:
SW319:
HW216:
HW215:
HW214:
If your last
University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MAT A23S
Winter 2012
Assignment #5
You are expected to work on this assignment prior to your tutorial in the
week of February 13th . You may ask questions about this assig
University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MAT A23S
Winter 2012
Assignment #4
You are expected to work on this assignment prior to your tutorial in the
week of February 6th . You may ask questions about this assign
University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MAT A23S
Winter 2012
Assignment #3
You are expected to work on this assignment prior to your tutorial in the
week of January 30th . You may ask questions about this assign
University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MAT A23S
Winter 2012
Assignment #2
You are expected to work on this assignment prior to your tutorial in the
week of January 23rd . You may ask questions about this assign
University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MAT A23S
Winter 2012
Assignment #1
You are expected to work on this assignment prior to your tutorial in the
week of January 16th. You may ask questions about this assignm
Eigenvalues and Eigenvectors
DEFINITION: Let A be an n n matrix. A scalar is an eigenvalue of A if there is a
nonzero vector v Rn , such that Av = v. In this case, v is called an eigenvector of A
corresponding to the eigenvalue .
How to Find the Eigenvalu
Linear Algebra Notes
Numbers
1.
N
= cfw_1, 2, 3, 4, is the set of natural numbers.
2.
Z
= cfw_0, 1, 2, 3, 4, is the set of the integers.
3.
Q
= cfw_ p | p, q Z and q = 0 is the set of the rational numbers.
q
4.
Q
= cfw_x R|x Q is the set of all irration
University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MAT A23
Summer 2015
Assignment #1
You are expected to work on this assignment prior to your tutorial in the
week of May 11th. You may ask questions about this assignment i
University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MAT A23
Summer 2015
Assignment #2
You are expected to work on this assignment prior to your tutorial in
the week of May 18rd . You may ask questions about this assignment
University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
Linear algebra I
MATA23 Winter 2016
Fraleigh & Beauregard, Pages 99 101
1
2
3
4
38. F T T T F F T T F T
5
Fraleigh & Beauregard, Pages 134 136
6
7
31. (See the text answ
University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
Linear algebra I
MATA23 Winter 2016
Fraleigh & Beauregard, Pages 84 86
1
2
Fraleigh & Beauregard, Pages 99 101
3
In addition:
1 1 2 1 1 2 1 0 2 1 0 2
1. a) A =
~
~
~
=
University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
Linear algebra I
MATA23 Winter 2016
Fraleigh & Beauregard, Pages 46 -48
1
37. Since hji = 1/(j + i 1) = 1/( i + j 1) = hij, therefore Hn is symmetric.
2
Fraleigh & Beaur
University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
Linear algebra I
MATA23 Winter 2016
Fraleigh & Beauregard, Pages15 -17
1
2
Fraleigh & Beauregard, Pages 31 -33
3
University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MATA23
Assignment 8
Summer 2015
Study: Sections 2.3 for this assignment. Read ahead in Sections 4.1 and 4.2 (cross product and
determinants).
Problems:
1. Section 2.3, Pag
University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MATA23
Assignment 7
Summer 2015
Study: Sections 2.1 and 2.2 are covered in this assignment. Read ahead in Sections 2.3 and 4.1.
See the Notes below too.
Problems:
1. Secti
University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MAT A23
Summer 2015
Assignment #9
You are expected to work on this assignment prior to your tutorial during
the week of July 13th-17th. You may ask questions about this as
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT A23
Summer 2015
Final Assignment
You are expected to work on this assignment prior to your tutorial in the
week of July 27th. You may ask questions about this assignment