McGill University
Department of Mathematics and Statistics
MATH 270 Applied Linear Algebra
Fall 2011
Assignment 6: Solutions
1. Consider the linear recurrence relation an+2 = 3an+1 2an .
(a) Find the
Middle of term quiz version 1., Math 270. Thursday Oct 24th. Do all 1
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work 111 Space pmwded. N0 calcuiafcors Show all you? work S 3 KM
, x . . 1 ~1 * w;
1. (10 marks) Prove that the set of ma
Middle of term quiz version 4, Math 270. Thursday Oct. 25th. Do all
work in space provided. No calculators. Show all your work
1. (5 marks) Prove or disprove: If V is an inner product space and v V
is
Math 270 nal exam version 1. Thursday Dec. 6th, 2012. 9am - noon.
Do all work in space provided. No calculators. Show all your work, except
for the multiple choice portion.
Multiple choice portion. 3
Middle of term quiz version 1, Math 270. Thursday Oct. 25th. Do all
work in space provided. No calculators. Show all your work
1. Consider the linear transformation F : R2 R2 for which F (1, 1) =
(3,
Namezmderline family name)
Student Number: Signature:
MCGILL U NIV ERSIT Y
FACULTY OF ENGINEERING
FINAL EXAMINATION
MATH 270
Applied Linear Algebra
Examiner: Professor D. Wise Bate: Monday Decembe
McGILL UNIVERSITY
FACULTY OF ENGINEERING
FINAL EXAMINATION
MATH 270
Applied Linear Algebra
Examiner: Professor J. Love 5 Date: Wednesday April 26, 2006
Associate Examine Prof 301' D. Wise Time: 2:00 P
Midterm Exam of Applied Linear Algebra - Math 270
March 9, 2011
Notation: Let Pn be the space of real polynomials of degree less or equal than n, e.g.:
P1 = cfw_ax + b, for a, b R, P2 = cfw_ax2 + bx +
McGILL UNIVERSITY
FACULTY OF ENGINEERING
FINAL EXAMINATION
MATH 270, Applied Linear Algebra 'Spring 2007
Date: Wednesday, April 25, 2007 Time: 9:00 am 12:00 pm
Examiner: Basak Giirel
Associate Examine
Linear algebra - Wikipedia, the free encyclopedia
3 of 5
http:/en.wikipedia.org/wiki/Linear_algebra
Some useful theorems
Every vector space has a basis.[3]
Any two bases of the same vector space have
Linear algebra - Wikipedia, the free encyclopedia
1 of 5
http:/en.wikipedia.org/wiki/Linear_algebra
Linear algebra
From Wikipedia, the free encyclopedia
Linear algebra is the branch of mathematics con
McGill University
Department of Mathematics and Statistics
MATH 270 Applied Linear Algebra
Fall 2011
Midterm Solutions
1. (10 points) Consider the set R2 together with the following operations:
(x, y)
McGill University
Department of Mathematics and Statistics
MATH 270 Applied Linear Algebra
Fall 2011
Assignment 3: Solutions
1. Consider the map L : Mat(n n, R) R, L(A) = trace(A), where Mat(n n, R) i
McGill University
Department of Mathematics and Statistics
MATH 270 Applied Linear Algebra
Fall 2011
Assignment 2: Solutions
2
4
3
1
1 3
5 1
1. Consider the subspaces S1 := span , , S2 :=
McGill University
Department of Mathematics and Statistics
MATH 270 Applied Linear Algebra
Fall 2011
Assignment 5: Solutions
1. Let A be an n n matrix with coecients in K.
(a) Prove that A is invertib
McGill University
Department of Mathematics and Statistics
MATH 270 Applied Linear Algebra
Fall 2011
Assignment 4: Solutions
1
2
1. Compute the determinant of A = 2
7
5
3 7 9 8
4 8 11 9
2 1
2 2.
7 3
McGill University
Department of Mathematics and Statistics
MATH 270 Applied Linear Algebra
Fall 2011
Assignment 1: Solutions
1. Let z, w C. Prove that zw = z w.
Solution:
Let z = x1 + iy1 , w = x2 + i
McGill University
Department of Mathematics and Statistics
MATH270 Applied Linear Algebra
COURSE OUTLINE
Instructor:
Dr. Sidney Trudeau, Burnside Hall 1243
E-mail: [email protected]
Office hours:
Linear algebra - Wikipedia, the free encyclopedia
2 of 5
http:/en.wikipedia.org/wiki/Linear_algebra
When I went to Edinburgh as a young lecturer in 1922, I was surprised to find how different the curr
Final exam of Applied Linear Algebra - Math 270
April 19, 2011
Problem 1
(2 pts.)
1
2
Find two dierent PLU decompositions for A =
2
1
.
SOLUTION:
1
A=
1
=
Problem 2
1
2
0
1
1
0
1
1/2
2
3
(1 pt.)
2
1
3