Final exam
MAT 1341C
1
(1) (3 pts) Let A be an m n matrix, let R be a row-echelon form of A.
(a) If B col(A), the linear system AX = B is solvable. True or false?
My answer:
(b) If A is a 4 7 matrix and R has precisely two rows of zeros, then the set of s
Test 1
MAT 1341C
February 14, 2012
1
(1) (6 pts) If the last entry of your student number is even take Aeven , otherwise take Aodd .
1
2 1
1 1 1
1 2
Aeven = 0
Aodd = 0 1 2
1 3 2
2 2 1
Find the inverse of your matrix and check your answer by verifying the
Assignment 2
MAT 1341C
due March 20, 2012, 13:00
1
(1) (6 pts) Let be the last digit of your student number. Which of the following is (are) subspaces?
Support your answer with details.
T
(A) U1 = x y z : x = 0 ,
(B) U2 = cfw_X R3 : AX = 3X, where A is a
Test 1
MAT 1341C
Feb. 11, 2010
1
(1) (a) (1 pt) A linear system with 4 variables and 5 equations always has innitely many solutions.
True or false? (No justication required)
Solution: This is false, since the system may not be solvable. For example, the r
Test 2
MAT1341D
(1) (2 pts) In the matrix below replace with
and calculate the determinant:
1
1
0
March 25, 2010
1
the second last digit of your student number
2
0 1
1 2
Solution: Expanding along the rst column, we get
1 2
1 0 1
0 1 2
=
0 1
1 2
+
2
1 2
University of Ottawa
Department of Mathematics and Statistics
MAT 1341C: Introduction to Linear Algebra
Instructor: Erhard Neher
Final Exam
Time: 3 hours
Family name (CAPITALS)
First name (CAPITALS)
Signature
Student number
Please read these instructions
Test 3
MAT 1341C
March 31, 2012
1
(1) (6 pts) Are the following statements true or false? Answer with T for true and F for false.
(a) One calls vectors X1 , X2 , . . . , Xk linearly independent if the following condition holds: Whenever all scalars s1 , .
Page 1
University of Ottawa
Department of Mathematics and Statistics
MAT 1341C: Introduction to Linear Algebra
Instructor: Erhard Neher
Test 2
(March 3, 2012)
Family name (CAPITALS)
First name (CAPITALS)
Signature
Student number
The last three digits of m
Test 2
MAT 1341C
March 3, 2012
1
(1) Replace be the second last digit of your student number. Find the scalar equation of the line
T
parallel to 1 0 and passing through P (3, 2, 5).
My answer:
T
Solution: Since the line is parallel to the vector d = 1 0 ,
Test 1
MAT 1341C
Jan. 28, 2012
1
(1) (2 pts) In the matrix below replace by the last digit of your student number. Find the matrix
A satisfying the following equation:
1 2
1 3
T
AT + 2 0 1
=
1 0 2
1 2
Solution: Since (AT )T = A, the left hand side of th
Page 1
University of Ottawa
Department of Mathematics and Statistics
MAT 1341C: Introduction to Linear Algebra
Instructor: Erhard Neher
Test 1
(Jan. 28, 2012)
Family name (CAPITALS)
First name (CAPITALS)
Signature
Student number
Please read these instruct
Page 1
University of Ottawa
Department of Mathematics and Statistics
MAT 1341 A: Introduction to Linear Algebra
Instructor: Monica Nevins
Assignment 9
Due November 27th, 2008 at 17:30 in the DGD (SITE H0104)
Family (Last) Name:
First Name:
Student Number:
Page 1
University of Ottawa
Department of Mathematics and Statistics
MAT 1341 A: Introduction to Linear Algebra
Instructor: Monica Nevins
Assignment 5
Due October 23th, 2008 at 17:30 in the DGD (SITE H0104)
Family (Last) Name:
First Name:
Student Number:
Page 1
University of Ottawa
Department of Mathematics and Statistics
MAT 1341C : Introduction to Linear Algebra
Instructor : Erhard Neher
Assignment 1 : due Jan. 19, 2010, 13:00 in the classroom
FAMILY NAME (CAPITALS)
F IRST NAME (CAPITALS)
Signature
Stud
MAT 1341B: Introduction to Linear Algebra
Instructor: Erhard Neher
Mini test 2
(November 19, 2004)
Family Name:
First Name:
Student number:
Please read these instructions carefully:
This is a closed book exam, and no notes of any kind are allowed. The us
MAT 1741 Test de pratique
Professeur : Abdelkrim El basraoui
1
Nom :
Choix multiples
C
2
3
Prnom :
e
A
D
4
Numro dtudiant :
e
e
5
Pour le correcteur
6
[Bonus] 7
Total
La dure de cet examen est 80 minutes.
e
Cet examen est ` livre ferm et vos notes de
Université d’Ottawa - University of Ottawa
Nom :
Prénom :
Numéro d’étudiant :
Faculty of Science
Mathematics and Statistics
Faculté des sciences
Mathématiques et de statistique
MAT 1741 C — Test 3 — V.A
Professeur : Abdelkrim El basraoui
12 novembre 2015
Assignment 2
MAT 1341 B (due October 11, 2007)
Page 3
1. (a) (2 points) In the matrices below replace by the last digit of your student number and calculate all
possible products between the two matrices
A=5
0
3
7
4
and B =
1 3
3 2
2
5
Answer: Since the f
Page 1
University of Ottawa
Department of Mathematics and Statistics
MAT 1341 B: Introduction to Linear Algebra
Instructor: Erhard Neher
Final Exam, Dec. 7, 2007
Family Name:
First Name:
Student number:
Please read these instructions carefully:
Read each
Page 1
University of Ottawa
Department of Mathematics and Statistics
MAT 1341 B: Introduction to Linear Algebra
Instructor: Erhard Neher
Assignment 5; due November 15, 2007, 17:30 in the class room
Family Name:
First Name:
Student number:
The last digit o
Page 1
University of Ottawa
Department of Mathematics and Statistics
MAT 1341 B: Introduction to Linear Algebra
Instructor: Erhard Neher
Assignment 4; due November 8, 2007, 17:30 in the class room
Family Name:
First Name:
Student number:
The last digit of
Dignstit: Test MAT 13-11 {Irving 8! RUDE?)
1. The area of the triangle with verticea .1f1.1,1}: BEN, 1= 2: and 'fl. U, 2] is
11.15."
?" {ET-EE- EE.§, Eiam?lc 11.
33x33 _
I: "'"? .-r T T
(":3 Aisio k 11 it t n} = DI. 1;] I]
1'];
A"? -~> 1- , 'I'
L5 Ill-EL"
Page 1
University of Ottawa
Department of Mathematics and Statistics
MAT 1341 B: Introduction to Linear Algebra
Instructor: Erhard Neher
Test 3; Nov. 22, 2007, 17:30-18:50
Family Name:
First Name:
Student number:
The last digit of your student number is =
Page 1
University of Ottawa
Department of Mathematics and Statistics
MAT 1341 B: Introduction to Linear Algebra
Instructor: Erhard Neher
Test 2; Oct. 25, 2007, 17:30-18:50
Family Name:
First Name:
Student number:
The last digit of your student number is =