University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MAT C44, Winter 2008
Solutions to Assignment #2
Problem 23. on page 155: The student needs to cross 24 intersections on her way to school.
On each intersection, she has
University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MAT C44, Winter 2008
Solutions to Assignment #4
Problem 2. on page 317: Let n be a set of all 2-by-n arrays
x11 x12 x1n
x21 x22 x2n
such that x11 < x12 < < x1n , x21 < x
University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MAT C44, Winter 2008
Solutions to Assignment #1
Problem 38. on page 24: The following is a symmetric, idempotent Latin square of order 3:
1 3 2
3 2 1
2 1 3
Now we shall
University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MAT C44, Winter 2008
Solutions to Assignment #3
Problem 11. on page 261: Lucas numbers are defined by the relation ln = ln1 + ln2 , and
l0 = 2, l1 = 1.
(a) We need to sh
University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MAT C34F
2013/14
Problem Set #4
Due date: Thursday, October 24, 2013 at the beginning of class
Do the following problems.
1. Find the Laurent expansion of (z 2 1)1 valid
University of Toronto Scarborough
Department of Computer and Mathematical Sciences
MAT C34F
2013/14
Problem Set #2
Due date: Thursday, September 26, 2013 at the beginning of class
1. For each arc C and function f find the value of
Z
C
f (z)dz :
f (z) = (z
University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MAT C34F
2013/14
Problem Set #5
Due date: Thursday, November 14, 2013 at the beginning of class
Do the following problems.
1. By considering the integral
Z
prove that
Z
MATC34 2013 Solutions to Assignment 2
1. f (z) =
Find
R
C
z+2
z
2
z
=1+
f (z)dz when C = (i)
C = cfw_z = 2ei , 0
The integral of 1 is
Z
dz =
2
z
The integral of
Z
0
2ei id = 2ei |0 = 2(2) = 4
is
Z
dz
=2
id = 2i
z
0
so the integral is 4 + 2i.
Z
2
(ii) C
University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MAT C34F
2013/14
Problem Set #3
Due date: Thurs Oct 10, 2013 at the beginning of class
1. Find the value of the integral of g(z) around the circle |z i| = 2 in the posit
University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MAT C34F
2013/14
Problem Set #6
Due date: Thursday, November 28, 2013 at the beginning of class
Do the following problems.
1. Find the images of (a) cfw_z : 0 < arg(z) <
MATC34 Solutions to Assignment 6
1. Find the images of
(a) cfw_z : 0 < arg(z) < /6
(b) D(0; 2)
(c) cfw_z : 0 < Im(z) < 1 under z 7 1/z.
Solution: Image under f : z 7 1/z of
(a) cfw_z : 0 < arg(z) < /6
= cfw_zrei : 0 < < /6 In this case z 1 = r1 ei : 0 < <
University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
MAT C34F
2013/14
Problem Set #1
Due date: Thursday, September 12, 2013 at the beginning of class
Reading: Priestley Chap. 1 and Chap 3
Solve the following problems.
1. P
MATC34 2013 Solutions to Assignment 1
1. f (z) = exp z
exp z)
exp(
z + h)
f (z + h) f (z)
= lim
h0
h0
h
h
lim
h
h0 h exp z
= lim
The limit does not exist.
2.
sin(z) = sin(x + iy) = sin(x) cosh(y) + i cos(x) sinh(y)
sin(z) = cosh(f )
if and only if
sin(x)
MATC34 2013 Solutions to Assignment 4
1. (a)
(z 2
1
1
=
1)
(z 1)(z + 1)
For 0 < |z 1| < 2,
(z 2
1
1
1
=
=
1)
(z 1)(z 1) + 2)
(z 1)2(1 + (z 1)/2)
Put w = (z 1)/2:
Since
X
1
(1)n wn
=
1 + w n=0
for |w| < 1,
(1 + w)1 =
X
(1)n wn
n=0
so
1
1X
(1)n wn1 .
(1 +
MATC34 2013 Solutions to Assignment 5
1.
Z
(0;1) 2z 4
ei iei d
2e4i + 5e2i + 2
0
d
R
2i
2e2i+5+2e
= i 02 i
=
=i
Z
2
0
z
dz
+ 5z 2 + 2
Z
2
8
=i
Z
2
0
(0;1) 2z 4
d
+ei
2
d
8 cos2 + 1
To compute
Z
e
2
4+5
zdz
+ 5z 2 + 2
This has poles when
z 4 + 5/2z 2 + 1 =
MATC34 2013 Solutions to Assignment 3
R
1. = cfw_|z i| = 2. So we need to compute g(z)dz where g(z) =
1
1
= (z2i)(z+2i)
. The pole at z = 2i is inside , while that at z = 2i
z 2 +4
is outside . So by the Cauchy integral formula, the integral is 2if (2i)
1
MATA23H3 TERM TEST
Linear Algebra I a.
x "-5
June 18 4. 5%,:
EXAMINER: B. McLellan
DURATION: 110 minutes
PART A: [20 TOTAL MARKS] MULTIPLE CHOICE: Circle one of fol
lowing (a)(e).
(1)[4 MARKS] Given the following statements:
I. If A, B 6 Mn are invertib
MATA 23H3
Tutorial Five
Summer 2013
For Tutorials on Tuesday June 11 and Wednesday June 12
Topics covered in this assignment are from part of Section 1.5 and part of Section 1.6 of the textbook.
Particularly, the following topics are covered:
Computation
University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
Term Test
MATA23H
Linear Algebra I
Examiner: S. Chrysostomou
Date: Friday, March 9, 2012
Duration: 110 minutes
FAMILY NAME:
GIVEN NAMES:
STUDENT NUMBER:
DAY AND TIME OF YO
MATA 23H3
Tutorial Ten
Summer 2013
For Tutorials on Tuesday July 23 and Wednesday July 24
Topics covered in this assignment are from part of Section 4.3 (Pages 265 - 270) and part of Section 5.1 (up
to and including Theorem 5.1 in Page 296). Particularly,
MATA 23H3
Tutorial Eight
Summer 2013
For Tutorials on Tuesday July 9 and Wednesday July 10
Topics covered in this assignment are from Section 2.3 and part of Section 2.4 (Pages 154-159) of the textbook.
Particularly, the following topics are covered:
The
MATA 23H3
Tutorial Nine
Summer 2013
For Tutorials on Tuesday July 16 and Wednesday July 17
Topics covered in this assignment are from Section 4.1, Section 4.2, and part of Section 4.3 (Pages 238 - 265)
of the textbook. Particularly, the following topics a
MATA 23H3
Tutorial Four
Summer 2013
For Tutorials on Tuesday June 4 and Wednesday June 5
Topics covered in this assignment are from Section 1.4 and part of Section 1.5 of the textbook. Particularly,
the following topics are covered:
c
Gauss Reduction of
MATA 23H3
Tutorial Six
Summer 2013
For Tutorials on Tuesday June 25 and Wednesday June 26
Topics covered in this assignment are from part of Section 1.6 and part of Section 2.1 of the textbook.
Particularly, the following topics are covered:
Structure of
University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
Linear algebra I
MATA23 Winter 2016
Fraleigh & Beauregard, Pages 300 - 302
1
2
3
Fraleigh & Beauregard, Pages 315 - 316
=
4
5
6
Answer to the addition:
768 1280
1.
.
25
University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
Linear algebra I
MATA23 Winter 2016
Fraleigh & Beauregard, Pages 271 - 273
1
2
3