Sophie Chrysostomou
Digitally signed by Sophie Chrysostomou DN: cn=Sophie Chrysostomou, o=UTSC, ou=Division of Computer and Mathematical Sciences, [email protected] utoronto.ca, c=CA Date: 2008
University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MATA23
Assignment 5
Summer 2016
Study: Sections 2.1 and 2.2 are covered in this assignment.
Terminology and Concepts
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT A23S
2014/2015
Assignment #7
You are expected to work on this assignment prior to your tutorial in the week of Marc
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT A23S
2014/2015
Assignment #6
You are expected to work on this assignment prior to your tutorial in the week of Febr
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT A23S
2014/2015
Assignment #5
You are expected to work on this assignment prior to your tutorial in the week of Febr
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT A23H
2014/2015
Solutions #5
1. (Fraleigh & Beauregard, pages 99 101)
(2) S = cfw_[x, x + 1] | x R. Clearly 0 = [0,
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT A23H
2014/2015
Solutions #6
1. (Fraleigh & Beauregard, pages 134 136)
(1) Two distinct nonzero vectors in R2 are de
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT A23H
2014/2015
Solutions #11
1. (Fraleigh & Beauregard, pages 300 303)
(18) T ([x, y]) = [x y, x + y] so T (e1 ) =
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT A23H
2014/2015
Solutions #4
x 2y
4x 5y
1. (a)
3 x + 3y
1 2
5
4 5
8
3 3
3
1 2
5
0
3 12
0
0 0
b1
i.e., if b = b2
b
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT A23H
2014/2015
Solutions #8
1. (Fraleigh & Beauregard, pages 165 166)
x
x
x
2
=
=A
R . Now TA
(1) The range
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT A23H
2014/2015
Solutions #1
1. (Fraleigh & Beauregard, pages 1517)
z
v+w
w
v
(3) v = [1, 3, 2] and w = [1, 2, 4] so
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT A23S
2014/2015
Assignment #3
You are expected to work on this assignment prior to your tutorial in the week of Janu
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
FINAL EXAMINATION
MATA23H3 - Linear Algebra I
Examiner: E. Moore
Date: April 10, 2015
Start Time: 9:00AM
Duration: 3 ho
Term Test
MATA23
Linear Algebra I
Date: March 2nd , 2016
Duration: 110 minutes
Examiner: Sophie Chrysostomou
Xiamei. Jiang
1. (12 points)
1) Let u = [2 + c, 3c, -1] and v = [6, 6, -3 + c].
a) Find all
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
Midterm Test
MATA23H3 Linear Algebra I
Examiners: E. Moore
K. Smith
Date: March 5, 2014
Duration: 100 minutes
1. [12 po
University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MATA23
Assignment 7
Summer 2016
Tutorial Quiz 4 is in Week 9 (July 4 - 8). You are responsible for knowing Assignmen
University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MATA23
Assignment 4 (2 pages)
Summer 2016
Work on the course material and problems below. Tutorial Quiz 2 takes plac
University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MATA23
Assignment 3
Summer 2016
Study: Section 1.5 (mostly) and 1.6 are covered in this assignment. You should also
MATA23 Quiz #5
Week 8
Name:
1
Student#:
More about Matrix! (10 points)
Given a matrix A such that
1
0
A=
3
2
3
2
11
5
0
4
4
3
1. Verify the rank equation.
2. Find a basis for the column space.
1
1 2
2
MATA23 Quiz #8
Week 11
Name:
1
Student#:
Cross Product (1 point)
Let a = [1,2,3], b=[4,5,6], find b(axb)
2
Calculating Determinants (9 points)
Indicate all the determinant properties that you used, if
MATA23 Quiz #3
Week 5
Name:
1
Student#:
Important Definitions (2 points)
1. Define row equivalent of two matrices A,B.
2. Given a square matrix A, what is the trace of A?
2
Gauss Jordan Method (4 poin
MATA23 Quiz #7
Week 10
Name:
1
Student#:
Understand a Linear Transformation (6 points)
Given a standard matrix representation of a linear transformation:
1 0
A=
0 1
1. Describe geometrically what does
MATA23 Quiz #2
Week 4
Name:
1
Student#:
Important Definitions (2 points)
1. Define the span of vectors.
2. Define the dot product of two vectors.
2
Vectors (6 points)
For the following 2 parts:let u=[
MATA23 Quiz #6
Week 9
Name:
1
Student#:
Verifying a Linear Transformation (3 points)
Is T([x1 , x2 ]) = [x1 x2 , x2 + 1, 3x3 5x2 ] a linear transformation of R2 R3 ? Why or why
not ?
2
The Linear Tran
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT A23S
2014/2015
Assignment #11
You are expected to work on this assignment prior to your tutorial in the week of
Mar
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT A23S
2014/2015
Assignment #4
You are expected to work on this assignment prior to your tutorial in the week of Febr
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT A23S
2014/2015
Assignment #9
You are expected to work on this assignment prior to your tutorial in the week of
Marc
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT A23S
2014/2015
Assignment #2
You are expected to work on this assignment prior to your tutorial in the week of Janu
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT A23H
2014/2015
Solutions #7
1. (Fraleigh & Beauregard, pages 152 154)
(1) Let x = [x1 , x2 , x3 ], y = [y1 , y2 , y
Definition: The algebraic multiplicity of an eigenvalue of A
is its multiplicity as a root of the characteristic polynomial.
The geometric multiplicity of is the dimension of its eigenspace
E .
Theore
University of Toronto Scarborough
Department of Computer & Mathematical Sciences
MAT A23S
2014/2015
Assignment #10
You are expected to work on this assignment prior to your tutorial in the week of
Mar