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Linear Equations - Linear Algebra - Exam, Exams of Linear Algebra

English and Foreign Languages UniversityLinear Algebra

This is the Exam of Linear Algebra and its key important points are: Linear Equations, Gauss Jordan Elimination, System, Solution, True or False, Statement, Matrices, Symmetric, Cramars Rul, Orthogonal Projection

Typology: Exams

2012/2013

Uploaded on 02/14/2013

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DAWSON COLLEGE
DEPARTMENT OF MATHEMATICS
FINAL EXAMINATION
LINEAR ALGEBRA 201-NYC-05 (Regular)
Winter 2011
Time: 3 hours
Examiners: G. Honnouvo, B. Szczepara
Student Name: ________________________________________________
Student ID Number: ___________________________________________
This examination contains 10 problems.
Each problem is worth the same amount.
#
Marks
1
2
3
4
5
6
7
8
9
10
Total
Term
Grade
pf3
pf4

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DAWSON COLLEGE

DEPARTMENT OF MATHEMATICS

FINAL EXAMINATION

LINEAR ALGEBRA 201 - NYC-05 (Regular)

Winter 2011

Time: 3 hours

Examiners: G. Honnouvo, B. Szczepara

Student Name: ________________________________________________

Student ID Number: ___________________________________________

This examination contains 10 problems. Each problem is worth the same amount.

# Marks

Total Term Grade

  1. Solve the following system by Gauss – Jordan elimination:

a) b)

  1. Consider the system of linear equations where:

, and

a) Find. b) Solve the system using.

  1. For which values of k will the following system have no solution? Exactly one solution? Infinitely many solutions?

2

  1. Find all matrices such that:

a) b)

  1. Determine whether the following statement is true or false. a) is symmetric for any matrices A and B. b) The planes and are perpendicular.

a) If is a 3x3 matrix such that then find: t t

b) Solv by Cram r’s Rul :

  1. Given the vectors.

a) Find the orthogonal projection of the vector u on the vector b) Find the constant k such that the vector is perpendicular to v.

ANSWERS:

  1. a) b)
  2. a) =

 ^  

b)

  1. a) b)
  2. a) True. b) True.
  3. a) (i) (ii) 32 b)
  4. a) b)
  5. a) b)

x

y t

z

  1. a) , b)
  2. a) b)