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Dawson College Mathematics Department Final Examination - December 2010, Exams of Linear Algebra

English and Foreign Languages UniversityLinear Algebra

A final examination paper from dawson college mathematics department, held on december 22, 2010. The exam consists of 18 questions covering various topics in mathematics, including algebra, determinants, cramer's rule, vectors, and geometry. Students are required to answer all questions directly on the examination paper and are permitted to use translation and regular dictionaries, as well as non-programmable calculators. The exam is worth 100 marks and contributes 50% to the final grade.

Typology: Exams

2012/2013

Uploaded on 02/14/2013

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Dawson College
Mathematics Department
Final Examination
201-105-DW
Wednesday, December 22, 2010
Student Name: ______________________________________________________
Student I.D. #: ______________________________________________________
Teacher: ___________________________________________________________
Instructors: L. Frajberg, G. Honnouvo, O. Zlotchevskaia
TIME: 14:00 – 17:00 (3 hours)
INSTRUCTIONS:
• Print your name and student I.D. number
in the space provided above.
• Attempt all questions.
• All questions are to be answered directly on
the examination paper.
• Translation and regular dictionaries are permitted.
• Small, noiseless, NON-PROGRAMMABLE calculators
without text storage or graphic capabilities are permitted.
• This examination consists of 18 questions.
• Please ensure that you have a complete exam package
before starting.
The exam must be returned intact.
Final Exam =_________________
or
50% Class Marks = _________________
+
50% Final Exam = _________________
Total = _________________
FINAL GRADE = __________________
Question # Marks
1/6
2/4
3/5
4/7
5/4
6/10
7/4
8/5
9/4
10/10
11/5
12/4
13/4
14/4
15/4
16/4
17/8
18/8
/100
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Download Dawson College Mathematics Department Final Examination - December 2010 and more Exams Linear Algebra in PDF only on Docsity!

Dawson College

Mathematics Department

Final Examination

201-105-DW

Wednesday, December 22, 2010

Student Name: ______________________________________________________

Student I.D. #: ______________________________________________________

Teacher: ___________________________________________________________

Instructors: L. Frajberg, G. Honnouvo, O. Zlotchevskaia

TIME: 14:00 – 17:00 (3 hours)

INSTRUCTIONS:

  • Print your name and student I.D. number

in the space provided above.

  • Attempt all questions.
  • All questions are to be answered directly on

the examination paper.

  • Translation and regular dictionaries are permitted.
  • Small, noiseless, NON-PROGRAMMABLE calculators

without text storage or graphic capabilities are permitted.

  • This examination consists of 18 questions.
  • Please ensure that you have a complete exam package

before starting.

The exam must be returned intact.

Final Exam =_________________

or

50% Class Marks = _________________

50% Final Exam = _________________

Total = _________________

FINAL GRADE = __________________

Question # Marks

1. (6 marks) If

and 1 1 ,

A B

find ) 3 2.

T i A B

ii AB

  1. (4 marks) If (^) ( )

2 , find.

7 3

T A A

4. (7 marks)

i) If

1

2 3 4 find

A A

−

by any method.

ii) Use your answer from i) to solve

1 2 3

1 2 3

1 2 3

x x x

x x x

x x x

ii) If A is a 3x3 matrix (^) ( )

2 det 3 given that det 2.

T find A A A =

iii) If (^) ( )

1 det A 2, what is det A 3 adj A? Assume A is 2 2. x

− = +

7. (4 marks)

If and det 5, find det where B= 4 4 4.

a b c g h i

A d e f A B d g e h f i

g h i a b c

9. (4 marks) Consider

( )

( )

k x y

x k y

For which values of k will the system have non-

trivial (non-zero) solutions?

10. (10 marks) Given the vectors u = [1, −1, 2 , ] v =[ 2,3,0]

r r

, find

i) vector w = 2 u − 3 v

ur r r

ii) a vector of length one (unit vector) which points in the opposite direction of v

r

iii) the cosine of the angle between u and v

r r

iv) the projection of onto ( )

v

u v proj u r

r r r

  1. (4 marks) Find the parametric equations of the line which passes through P (^) ( 1, −1, 2 (^) )and

is perpendicular to the plane whose equation is − 4 x + 3 y + z + − 10 = 0.

  1. (4 marks) Find the equation of the plane through P (^) ( 4, −2,1 (^) )which is parallel to both

u = [ 2,1,3]

r

and v = (^) [ 1, −2,0]

r

15. (4 marks) Consider the two lines whose respective parametric equations are

1 2 and 3

x t x s

y t y s

z t z s

Find the intersection point of the two lines.

  1. (4 marks) Find the distance from the point P (^) ( 3, −2, 4 (^) )to the plane − 2 x + 5 y + z − 6 = 0

18. (8 marks) Minimize

z = 4 x 1 (^) + 3 x 2

subject to the constraints

( )

1 2

1 2

1 2

x x

x x

x x