School

University of Calgary
Department

Mathematics

Course Code

MATH 211

Professor

Claude Laflamme

Study Guide

Midterm

Faculty of Science

Department of Mathematics & Statistics

MATH 211 – LINEAR METHODS I – FALL 2012

MIDTERM 1

Exam version: Practice

COURSE INFORMATION AND STUDENT IDENTIFICATION

INSTRUCTOR SECTION LAB STUDENT I.D. FIRST LAST

NAME NUMBER NUMBER NUMBER NAME NAME

EXAMINATION RULES

1. No Calculators, electronic equipment, or paper material other than this examination and scantron

sheet allowed.

2. Use the back of the previous page for rough work or calculations.

3. Students arriving late will not normally be admitted after one-half hour of the examination time has

passed.

4. No candidate will be permitted to leave the examination room until one hour has elapsed after the

opening of the examination.

5. All enquiries and requests must be addressed to supervisors only.

6. Candidates are strictly cautioned against:

(a) speaking to other candidates or communicating with them under any circumstances whatsoever;

(b) bringing into the examination room any textbook, notebook or memoranda not authorized by

the examiner;

(c) making use of calculators and/or portable computing machines not authorized by the instructor;

(d) leaving answer papers exposed to view;

(e) attempting to read other students’ examination papers.

The penalty for violation of these rules is suspension or expulsion or such other penalty as may be

determined.

7. Discarded matter is to be struck out and not removed by mutilation of the examination answer book.

8. Candidates are cautioned against writing in their answer books any matter extraneous to the actual

answering of the question set.

9. A candidate must report to a supervisor before leaving the examination room.

10. Answer books must be handed to the supervisor-in-charge promptly when the signal is given. Failure

to comply with this regulation will be cause for rejection of an answer paper.

MATH 211 ALL SECTIONS - MIDTERM 1 Fall 2012

Exam version: PracticePart A: Mark your answers on the scantron sheet provided.

Each question is worth 2 points.

1. What can you say about the general solution of the following system:

x+ 2y+ 3z+ 4w= 5

2x+ 4y+ 6z+ 8w= 11

(a) It has no solution.

(b) It has one solution.

(c) It has three solutions.

(d) It has inﬁnitely many solutions.

(e) None of the above.

2. What can you say about the general solution of the following system:

2x1+ 3x2−4x3+ 6x4= 0

2x1+ 3x2−5x3+ 6x4= 0

2x1+ 3x2−4x3+ 7x4= 0

(a) It has no solution.

(b) It has one solution.

(c) The general solution involves one parameter.

(d) The general solution involves two parameter.

(e) None of the above.

3. Which of the following options constitute the general solution of the following system of linear

equations:

x−y−z= 0

x+y+z= 4

(a) x= 3,y= 2,z= 1

(b) x= 2,y= 1,z= 1

(c) x= 2,y= 2 −s,z=s

(d) x= 2,y= 2 + s,z=s

(e) None of the above.

Page 2

MATH 211 ALL SECTIONS - MIDTERM 1 Fall 2012

Exam version: Practice

4. Express the general solution of the following system as a linear combination of basic solutions.

x1+ 2x2+ 4x3+x4= 0

x1+ 2x2+ 5x3+ 2x4= 0

(a) s[−2 1 0 0]T.

(b) t[1 1 −1 1]T.

(c) s[−2 1 0 0]T+t[3 0 −1 1]T.

(d) s[−2 1 0 0]T+t[4 −1 0 0]T.

(e) None of the above.

5. Find the rank of the following matrix:

1−2 1

2−4 2

−3 6 2

(a) The rank is 0.

(b) The rank is 1.

(c) The rank is 2.

(d) The rank is 3.

(e) None of the above.

6. The rank of the augmented matrix of the following system of linear equations

x+ 2y+ 3z= 0

x+ 2y+ 3z= 5

is:

(a) 0

(b) 1

(c) 2

(d) 3

(e) None of the above.

Page 3

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