University of Toronto at Scarborough Department of Computer and Mathematical Sciences
Linear algebra II
MATB24 Fall 2010 Section 1.4
29. F F T T F T T T F T
1
Section 1.5
2
Section 4.2
3
Addition: 1)
University of Toronto at Scarborough Department of Computer and Mathematical Sciences
Linear Algebra II
MATB24 Fall 2010 Assignment # 12 with the solution set This assignment covers lectures in week 1
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B24H
2014/2015
Term Test Solutions
1. (a) From the lecture notes we have
Definition: A field F is a set on which tw
University of Toronto at Scarborough Department of Computer and Mathematical Sciences
Linear Algebra II
MATB24 Fall 2010 Assignment # 2 You are expected to work on this assignment prior to your tutori
Term Test MATB24 Linear Algebra II
2009
1. (10 points)
. a) Give the definition of a field. b) Let K be a vector space over Z2 with basis cfw_1, t, so K = cfw_a + bt | a, b Z2. It is known that K beco
1. a) A field is a set F equipped with two binary operations addition and multiplication satisfy the following properties: addition: AA1: a + (b + c) = (a + b) + c AA2: a+b=b+a AA3: 0, s.t. a + 0 = a
Lecture 6 Thm: Let V , V be finite-dimensional vector spaces and T : V V is an isomorphism. If B 1 , b2 , ., bn is any basis of V, then (b1 ), T (b2 ), ., T (bn )is a basis b T of V .
6.1 Matrix repre
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
Midterm Test
MATB24H Linear Algebra II
Examiner: E. Moore
Date: October 25, 2013
Duration: 110 minutes
1. [11 points]
(
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B24H3
2015/2016
Assignment #7
You are expected to work on this assignment prior to your tutorial in the period Octo
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B24H3
2015/2016
Assignment #5
You are expected to work on this assignment prior to your tutorial in the period Octo
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
Midterm Test
MATB24H Linear Algebra II
Examiners: X. Jiang
E. Moore
Date: October 24, 2014
Duration: 110 minutes
1. [10
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B24H3
2015/2016
Assignment #8
You are expected to work on this assignment prior to your tutorial in the period Nove
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B24H3
2015/2016
Assignment #9
You are expected to work on this assignment prior to your tutorial in the period Nove
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B24H3
2015/2016
Assignment #6
You are expected to work on this assignment prior to your tutorial in the period Octo
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B24H3
2015/2016
Assignment #10
You are expected to work on this assignment prior to your tutorial in the period Nov
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B24H3
2015/2016
Assignment #6
You are expected to work on this assignment prior to your tutorial in the period Octo
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B24H3
2015/2016
Assignment #2
You are expected to work on this assignment prior to your tutorial in the week of Sep
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B24H3
2015/2016
Assignment #10
You are expected to work on this assignment prior to your tutorial in the period Nov
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B24H3
2015/2016
Assignment #4
You are expected to work on this assignment prior to your tutorial in the period Octo
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B24H3
2015/2016
Assignment #3
You are expected to work on this assignment prior to your tutorial in the week of Sep
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B24H3
2015/2016
Assignment #10
You are expected to work on this assignment prior to your tutorial in the period Nov
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B24H3
2015/2016
Assignment #11
The Final Examination will take place on December 19, from 2 pm 5 pm
Final Exam Room
2008 Term Test
MATB24 Linear Algebra II
1. (10 points)
. a) Give the definition of a general vector space.
b) Let V be the set of 2 2 matrices with zero determinant, with the usual matrix addition
and
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B41H
2016/2017
Assignment #7
This assignment is due at
November 11 November 17, 2016.
the
start
of
your
tutorial
in
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT B41H
2016/2017
Assignment #6
This assignment is due at
November 4 November 10, 2016.
the
start
of
your
tutorial
in
S4:
S3:
S2:
S1:
A4:
A3:
A2:
1
a
(v)
a (b c) a b a c
2
(iv) For each a in and each nonzero b in , there are elements c and d
in such that a c 0 and b d 1
(iii) There are elements 0 and 1 in such that 0
0 if and only if v = 0.
rv , w
An inner product space is a vector space V together with an
inner product on V .
0 if and only if v = 0.
v , rw
u, v u, w
(iv) v, v t 0 and v, v
(iii) r v, w
(ii) u, v w
u v w = u v w
0 and we write w = v
r s v = r v s v
(viii) if 1 is the multiplication identity in F then 1 v
(vii) r ( s v ) = (rs ) v
(vi)
(v) r v w = r v r w
vw
v.
(iv) For each v in V, there exists