Mon.April 14th 2008-2:00 pm
Final Math 123-08
1.(14 marks)Find the inverse of the matrix A by using appropriate row reduction of [ A|I ]
123
A= 2 3 4
121
-1
Hence show that A A = I. Use the above result to find the solution of ,
x1 + 2 x2 + 3 x3 = 1
2 x1
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1
NOTES FOR
MATH 123
LINEAR ALGEBRA and PROBABILITY
William J. Anderson
McGill University
These are not ocial notes for Math 123. They are intended for Andersons section,
but may be used by all, and are similar to the notes projected in class.
2
Contents
McGill University
Department of Mathematics and Statistics
MATH123 Linear Algebra and Probability
COURSE OUTLINE
Instructor:
Sidney Trudeau Burnside Hall 1243
Mahmood Sohrabi Burnside Hall 1126
E-mail: trudeau@math.mcgill.ca
E-mail: sohrabi@math.mcgill.ca
Math 123 Midterm Examination Version 2 Thursday February 26, 2015.
1. Kate invests $10 000 received from her grandmother in three ways.
With one part, she buys savings bonds at an interest rate of 2.5%
compounded annually. She uses the second part. which
McGILL UNIVERSITY
FACULTY OF SCIENCE
FINAL EXAMINATION
MATH 123
Linear Algebra and Probability
Examiner: Sidney Trudeau Date: Tuesday April 17, 2007
Associate Examiner: Igor Wigman Time: 2:00PM —5:00PM
INSTRUCTIONS
1. Please answer questions in the exam b
Math 123 Midterm Examination Version 2. Show all your work.
1. (5 marks each) Solve the following systems, or show no solution exists.
(a)
4x+4y—4z=4
2x—y+z=——3
x—2y+3z=2
I I I-/ I l"/ I
2.) / ’3 a 0‘3 3 ‘5 _) 0 ‘3 3‘5
/-2 3 Z 0—3 4- I 0 o I 6
/ I *I I /
Math 123 Midterm Examination Version 1. Show all your work.
1. (5 marks each) Solve the following systems, or show no solution exists.
(a)
4x+4y—4z=24i
m—2y+3z=
. ~16
)l‘l,6 )1—) 6 l’ x
2-, I ~9-> 0—3 3 -2/ 7: 0‘3 3-2!
/,23/ 6.3.9 ‘5 001/6
. /_/6 ‘ /-l‘6
Math 123 Supplemental\Deferred Exam. August 2010. Do all questionﬁ
in space provided. Nonugraphing, non—programmable calculators are allowed.
1. (‘20 marks) Solve the following systems of linear equations:
(a
222+y+z+3w=1
3x—22+2w=—1
5x+y—z+5w:0
7x+2y+8w=
MATH 123
Written assignment(2)
Due date:April 3 in the class
1. An urn contains 10 marbles: 4 red and 6 blue. A second urn contains 16 red marbles
and an unknown number of blue marbles. A single marble is drawn from each urn.
The probability that both mar
MATH 123
Written assignment(1)
Due date:March 7 in the class
1. Consider the following system of linear equations:
x1
2x1
2x2
x2
+ 2x2
2x2
+ 3x3
x3 + x4
2x3 + 4x4
3x3 + x4
=
=
=
=
1
2
3
4
Write the above system as a matrix equation AX = B
(Find A, X
Math 123 Supplemental\Deferred Exam. August 2010. Do all questions
in space provided. Non-graphing, non-programmable calculators are allowed.
1. (20 marks) Solve the following systems of linear equations:
(a)
(b)
2x + y + z + 3w = 1
3x 2z + 2w = 1
5x + y
Midterm Examination
MATH 123
Version 3
1
Student Number :
Section Number:
Last Name (PRINT) :
Other name(s):
MATHEMATICS 123 MIDTERM EXAMINATION
VERSION 3
INSTRUCTIONS
1. Check that this paper has a total of 6 pages, which includes this cover, 3 pages of
Midterm Examination
MATH 123
Version 2
1
Student Number :
Section Number:
Last Name (PRINT) :
Other name(s):
MATHEMATICS 123 MIDTERM EXAMINATION
VERSION 2
INSTRUCTIONS
1. Check that this paper has a total of 6 pages, which includes this cover, 3 pages of
Midterm Examination
MATH 123
Version 1
1
Student Number :
Section Number:
Last Name (PRINT) :
Other name(s):
MATHEMATICS 123 MIDTERM EXAMINATION
VERSION 1
INSTRUCTIONS
1. Check that this paper has a total of 6 pages, which includes this cover, 3 pages of
McGill University
Department of Mathematics and Statistics
MATH123 Linear Algebra and Probability
COURSE OUTLINE
Instructors:
Professor Anderson, BH 1245
Dr. Sidney Trudeau, BH 1243
E-mail: anderson@math.mcgill.ca
E-mail: trudeau@math.mcgill.ca
Restrictio
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