UNIVERSITY OF WINNIPEG
November 2011
DETERMINANT WORKSHEET
TOTAL PAGES: 7
Page 1 of 7
DEPARTMENT & COURSE NUMBER: MATH 1201
NAME: (Print in ink)
STUDENT NUMBER:
Q.1 Calculate the determinant of A. After doing this, calculate the transpose of A and its
det
UNIVERSITY OF WINNIPEG
19 October 2011
MIDTERM EXAMINATION
TOTAL PAGES:
Page 1 of 6
DEPARTMENT & COURSE NUMBER: MATH 1201
EXAMINATION: Linear Algebra I
TIME: 50 Minutes
EXAMINER: B. Penfound
NAME: (Print in ink)
STUDENT NUMBER:
SIGNATURE: (in ink)
(I unde
UNIVERSITY OF WINNIPEG
24 September 2012
TOTAL PAGES: 1
PROOFS TO KNOW
Page 1 of 1
DEPARTMENT & COURSE NUMBER: MATH 1201
EXAMINATION: Linear Algebra I
1. Provided the operations below work, you should be able to prove the following matrix properties (you
Q.1 Please use Figure 1 to help you answer Question 1.
150
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UNMSO X: ~+ NW
(2] (1] x-QO 7kg; i» :00
[3] we W XP 5
x3.
Figure 1: A Hypothetical Trafc Flow
[3] (3.) Suppose that Figure 1 represents the hypothetical ow of traio through a trafc c
UNIVERSITY OF WINNIPEG
22 October 2012
PROOFS TO KNOW - Section 002
TOTAL PAGES: 1
Page 1 of 1
DEPARTMENT & COURSE NUMBER: MATH 1201
EXAMINATION: Linear Algebra I
1. If A is invertible, then its inverse is unique.
2. If A is invertible, then At is inverti
UNIVERSITY OF WINNIPEG
21 November 2011
MIDTERM EXAMINATION
TOTAL PAGES: 7
Page 1 of 7
DEPARTMENT & COURSE NUMBER: MATH 1201
EXAMINATION: Linear Algebra I
TIME: 50 Minutes
EXAMINER: B. Penfound
NAME: (Print in ink)
STUDENT NUMBER:
SIGNATURE: (in ink)
(I u
Stuffs to know for Test #2
COMPUTATIONS:
-know how to find the inverse of a matrix using the
[A|I] -> [I|A-1] method (for 2x2, 3x3 or 4x4)
-know how to find the inverse of a matrix using the adjoint
formula (for 2x2 and 3x3); you are allowed to use the 2x
[8] Q.1 Solve the fdilowing system using Gauss-Jordan Elimination. Indicate what tye of solution
you obtain and whether the system is consistent or inconsistent.
22:; m 3:5 + y z = 0
3w + a: 23,: + z = 0
2w + 6x + 3; ~ z = 0 [5]Q.2(a) Let A be an m X n ma
UNIVERSITY OF WINNIPEG - MATH 1201
23 Mo-vember 2012
MOCK TEST #1
Question 1 designed by Kezia and Bretton:
Q.1 Let u = (3, 4) and v = (1, 3) be vectors in R2 .
(a) Determine u v.
(b) Calculate the cosine of the angle between the two vectors.
Question 2 d
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Complex Numbers
The complex number system is an algebraic system which contains the real numbers as well as an imaginary unit, a number denoted by i, which has the property
that i2 = 1. (We note that the real number system contains no number whose
square
MATH-1201 Linear Algebra I
Final Exam Review
Your nal exam covers material from the following sections:
Sections 1.1 - 1.10, Sections 2.1 - 2.5, Sections 3.1 - 3.5,
and the handout on Complex Numbers that was given in class.
You are responsible for the pr
,1
mm '
UNIVERSITY OF WINNIPEG - MATH 1201
14 November 2012 MIDTERM #3
TOTAL PAGES: 7 Page 1 of 7
COURSE: MATH 1201 TIME: 50 Minutes
NAME: (Print in ink)
STUDENT NUMBER:
SIGNATURE: (in ink)
(I understand that cheating is a serious oense)
INSTRUCTIONS