EMU  Department of Mathematics
MATH 241: Ordinary Dierential Equations And Linear Algebra,
MIDTERM I
(Fall 20102011)
Student no.:
1
2
Name:
3
4
5
6
Total
Please sign here:
Duration: 100 mins.
Important notes: Total number of questions in this examinatio
Eastern Mediterranean Universit
Department of Chemistry
Chem 101 General Chemistry
Fall 20112012 Quiz I
21/10/2011 16.3017.00
Student No: Q1
NameSurname: Q2
Group: Q3
Signature: Q4
Instructors: Prof. Dr. Huriye Icil (Gr. 1, 4)
Assist. Prof. Dr.
E.M.U.  FACULTY OF ARTS AND SCIENCES
DEPARTMENT OF MATHEMATICS
MATH
106  Linear Aieebra
Final Examination

28th of May 201
1
Duration: 2 hours.
NameSurname
Qr
Student no.
o1
o1
Signature
Q4
Group
o6
Qs
Total;
Remark: Ouestions 4 and 6 are also Ouiz 4
tE astern ful e frterrane
27 April
an'U niv ersity
2olt
(D ep artm
ent of fuL at ficmatic s
lylotfr 106 Linear afue1ra
2.Q?iz
Auratian: 45 ninutes
a? v\c
Q1
\
125
Question l.Show that
if
'lotaI
Q.i
/30
l1t0
155
4 and v are orthogonal vectors in R' such t
1. Consider the linear transformation
given by
a) Find the matrix of T.
b) Is T onetoone? Why or why not?
Row reducing A gives two pivots. Since there are 3 columns, there is a free variable, so T
is NOT onetoone
2.
a.
3.
4.
Math 106, solved questions. First list
1. Solve, by any method, the following linear system
y 2z =
x +
x 2y +
2x +
1
z =
0
z = 1
y +
.
Solution: The augmented matrix of the system is
successively:
1
1 2
1 2
1
2
1
1
1 2
1
0 3
0
0
3
0
1
1
1 2
1
1 2
2
1
1
Math 106, solved questions. Second list
1. Let x, y be two real numbers. Compute the determinant
y x y
x
y x y
x
x y
y
x
Solution:
x
x
y x
0
0
0
0
y x y
x
y x y
y x y
x
x y
x
y
=
y x
x
.
y
x y
x
y
y
= 0.
y x
x
y
R3 +R1 R1
1 0 1
2. Compute the determinant
MATH 106, Makeup Examination, Fall Semester, 2004. Solutions
(1) (a) Compute, when is possible, D + E, B C, A + C, AB, CB, CC T , tr(DT E T ),
tr(AB), where
3
A= 2
4
0
1 , B =
1
3
2
2
0
Solution: D + E =
3
0
2
6
2
2
1
3 .
4
1
2
, D = 1
2
0
4 , E =
1
2
MATH 106
Midterm Examination, Fall Semester 2004.
Solutions
Q1 (i) Solve, by any method, the system
3x
y +
z =4
(1)
x + 7y 2z = 1
2x + 6y
z =5
(ii) Find a nonnegative integer k as well as elementary matrices E1 , E2 , . . . , Ek such that
Ek Ek1 . . .
MATH 106
Final Examination, Fall Semester, 2004. Solutions
x + ky = 1
(1) (a) Determine for what values of k R the linear system
has
kx + y = 1
no solution, unique solution and innitely many solutions. When the system has
solution(s), write down the (gene
Math 106 Linear Algebra
November 5, 2012
MidTerm 1
EASTERN MEDITERRANEAN UNIVERSITY
FACULTY OF ARTS AND SCIENCES
MATHEMATICS DEPARTMENT
20122013 FALL SEMESTER
NameNameSurname
Student Number
Q1
Q2
Q3
Question 1.
method
(20 points)
Q4
Q5
Group No
Q6
Tota
1
MATH 106 Linear Algebra Quiz 1 SOLUTIONS
NameSurname
Q1
40
Student No
Q2
60
Total
100
Group No
Signature
March 19, 2012. Duration is 45 minutes.
Question 1)
Find a 3 1 matrix X with entries not all zero such that AX = 3 X , where
1 2 1
A = 1 0 1 .
4 4
Mathematics Formulary
By ir. J.C.A. Wevers
c 1999, 2008 J.C.A. Wevers
Version: May 4, 2008
Dear reader,
This document contains 66 pages with mathematical equations intended for physicists and engineers. It
is intended to be a short reference for anyone wh