Winter Term, 2006
I
Name:
S lL.Gn4a
Student Number:
Section:
WILFRID LAURIER UNIVERSITY
Waterloo, Ontario
Mat hematics 122 - Introductory Linear Algebra
Test I1 - March 15, 2006
Instructors:
Section F - 8:30 am - U. C elmins
Section H - 8:30 am - I. Ncube
Due: Oct 28/29 (in class)
Team Name(Please print) :
solution
presentation
possible
15
2
total
MA122 Assignment #6
mark
17
1. A matrix A is symmetric, if AT = A.
(a) Prove that if matrix A is symmetric, then A must be square.
(b) Let B be an m n matrix. Pr
Team Name(Please print) :
Due: Nov 18/19 (in class)
solution
presentation
possible
17
2
total
MA122 Assignment #9
mark
19
0 2 0
1. Write the matrix A = 1 0 3 as a product of elementary matrices.
2 0 5
1
2. Let A and B be invertible matrices. Prove that (5
MA122 Pre-Lecture Preparation for Week 2
(Remember that weeks start on Thursdays.)
Section 1.2
1. What does it mean for a set of vectors to be linearly dependent?
2. What does it mean for a set of vectors to be linearly independent?
Section 1.3
1. How do
solution
presentation
5
1. (a) Find all eigenvalues of A = 0
-2
mark
18
Not to be handed in
Team Name(Please print) :
possible
16
2
total
MA122 Assignment #12
0
1
0
-2
0 .
2
(b) Find a basis for the eigenspace corresponding to each eigenvalue.
(c) Give th
MA122 Pre-Lecture Preparation for Week 4
(Remember that weeks start on Thursdays.)
Section 2.1
1. What does it mean for an equation to be linear?
2. What are the coecients of a linear equation?
3. How do we determine if x Rn is a solution to a linear equa
Due: Nov 25/26 (in class)
Team Name(Please print) :
solution
presentation
possible
13
2
total
MA122 Assignment #10
mark
15
1 2 0
1. Using the determinant nd the value(s) of k for which A = k 1 k is invertible.
0 2 1
2. Let A be an n n matrix. Prove that i
Team Name(Please print) :
Due: Dec 2/3 (in class)
solution
presentation
possible
11
2
total
MA122 Assignment #10
mark
13
1. Suppose that A = [a1 a2 . . . an ] is an invertible n n matrix. Prove using Cramers Rule that the
system of equations Ax = aj has t
MA122 Pre-Lecture Preparation for Week 3
(Remember that weeks start on Thursdays.)
Section 1.4
No preparation needed.
Section 1.5
u1
v1
1. How do we calculate the cross-product of two vectors u = u2 and v = v2 ?
u3
v3
2. How do we calculate the scalar
MA122 Pre-Lecture Preparation for Week 5
(Remember that weeks start on Thursdays.)
Section 2.3
No preparation needed.
Section 3.1
1. How do we determine if two matrices are equal?
2. What is the denition of a square matrix?
3. What does it mean for a squa
Zhou Wang
Assignment Assignment 1 W14 due 01/19/2014 at 11:59pm EST
1. (1 pt)
Solve the system of linear equations using the substitution or
elimination method:
MA122 W14
If there is one solution, give its coordinates in the answer spaces
below.
If there
Team Name(Please print) :
Due: Nov 11/12 (in class)
solution
presentation
possible
11
2
total
MA122 Assignment #8
mark
13
1. Find a basis for the range and a basis for the nullspace of the mapping L : R4 R3 given by
L(x1 , x2 , x3 , x4 ) = (x1 + x4 , x2 2
Team Name(Please print) :
Due: Nov 4/5 (in class)
solution
presentation
possible
11
2
total
MA122 Assignment #7
mark
13
1. (a) Find the standard matrix of the reection in R3 through the plane 2x1 + x2 x3 = 0.
(b) Use the standard matrix found in part(a) t
MA122 Test II
March 10, 2004
Page 1 of 1
[12 marks ] 1. In 3-space, given points A(2, 4, 1), B (3, 0, 9) and C (1, 4, 0).
(a) Find the angle = BAC .
(b) Find the orthogonal projection of AB on AC .
(c) Find the area of the triangle having vertices A, B, C
Due: Oct 7/8 (in class)
Team Name(Please print) :
solution
presentation
possible
13
2
total
MA122 Assignment #4
mark
15
1. Determine the rank of the cocient matrix of the following homogenous system. Determine the
number of parameters in the general solut
MA122 Mock Final Exam
Name:
* Please remember that mock tests are meant as a means of providing an extra set of practice questions
and basis for a review class. Do not study for the midterm based solely on the topics covered by the mock
test! Go back thro
Due: Sep 23/24 (in class)
Team Name(Please print) :
solution
presentation
possible
13
2
total
MA122 Assignment #2
mark
15
1. Find the value of k so that the planes 2x1 + 5x2 + 4x3 = 5 and x1 + kx2 8x3 = 33 are perpendicular.
2. Let v Rn . Prove that cfw_v
solution
presentation
possible
14
2
total
MA122 Practice Assignment #3
mark
16
Due: Sep 30/Oct 1 (in class)
Team Name(Please print) :
1. Use a projection to nd the point in the given plane which is closest to the point Q(2, 3, 6).
3
2
0
2 + t1 1 + t
MA122 Recommended Problems
Below is a list of recommended practice problems taken from Introduction to Linear Algebra
for Science and Engineering, by Daniel Norman and Dan Wolczuk (2nd edition). These are not
to be handed in and are for your practice.
The
Team Name(Please print) :
Due: Oct 20/21 (in class)
solution
presentation
possible
14
2
total
MA122 Assignment #5
mark
16
0
2
6
1 3 0
1. Determine whether the set of vectors B = , , is a basis for the hyperplane with
0
1
3
0
1
1
equation x1 + 2x3
Fall Term, 2014
MATHEMATICS 122A, B&C Introductory Linear Algebra
Instructor: Mr. Shane Bauman
E-mail: [email protected]
Office: BA303E (Bricker Academic)
Office Hours: Mon, Tues, Wed 2:30-3:50 pm
All communication by e-mail only. I do not check MLS e-mail.
Fall Term, 2016
First Name:
Surname:
Section: A
WILFRID LAURIER UNIVERSITY
Waterloo, Ontario
MA 122 Introductory Linear Algebra
Midterm September 29, 2016
SOLUTIONS
Instructors:
Time Allowed: 80 minutes
Total Value: 90 marks
Number of Pages: 6 plus cover