2014-15 First Semester
MATH 2101 Linear Algebra I
Assignment 1
Due date: 17 Sept 2014 17:00
1. For each of the matrices A below,
transform it to reduced row-echelon form;
nd the rank of A;
solve the system Ax = 0.
1 3 5 7
(a) A = 3 5 7 9
5 7 9 1
1 0 1
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH2101: LINEAR ALGEBRA I
9:30 am- 12:00 noon
December 13, 2013
Only approved calculators as announced by the Examinations Secretary can be used in this
examination. It is candidates' responsibility t
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH 2101: LINEAR ALGEBRA I
9:30 am
May 29, 2014
~
12:00 noon
Only approved calculators as announced by the Examinations Secretary can be used in this
examination. It is candidates' responsibility to e
MATH 2101
Linear Algebra I
Sample Test 2
Name:
For Markers Use Only
University No
Q1
Q2
Q3
Q4
Q5
Total
Important Notes:
Fill in your name (exactly as on student card) and university number above.
Answer Questions 1 and 2 in the boxes below, and Question
2014-15 First Semester
MATH 2101 Linear Algebra I
Test 1
Name:
For Markers Use Only
University No
Q1
Q2
Q3
Q4
Q5
Total
Important Notes:
Fill in your name (exactly as on student card), tutorial group and university number
above.
Answer Questions 1 and 2
201415 First Semester
MATH 2101 Linear Algebra I
Test 1 Report
A.
Statistics
Score Distribution
Score Range
2029
3039
4049
5059
6069
7079
8089
9099
No of students
1
4
11
16
18
13
5
2
Item statistics
Question
1
2
3
4
5
Mean score
17.89
13.43
12.91
6.13
9.1
MATH 2101
Linear Algebra I
Sample Test 1
Name:
For Markers Use Only
University No
Q1
Q2
Q3
Q4
Q5
Total
Important Notes:
Fill in your name (exactly as on student card), tutorial group and university number
above.
Answer Questions 1 and 2 in the boxes bel
2015/16 First Semester
MATH 2101 Linear Algebra I
Chapter 1: Matrices, Vectors and Systems of Linear Equations
Coverage of Chapter 1:
Sections 1.1 to 1.4 as well as 1.6 and 1.7 will be covered.
You should read Section 1.5 by yourself.
A.
A Glimpse at the
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH2101 Linear Algebra I
Tutorial 9 Solutions
1. (a) The characteristic polynomial of A is
3t
2
det (A tI) = det [
] = (3 t)(2 t) (2)(3) = t2 t 12.
3
2 t
(b) We have
15 2
3
A2 A 12I = [
][
3 10
3
2
12
2014-15 First Semester
MATH 2101 Linear Algebra I
Extra Practice Problems 2
In each question, you answer by adding up the numbers of the correct statements. (For
example, if the statements are numbered 1, 2, 4, 8 and the rst three are correct, the answer
2014-15 First Semester
MATH 2101 Linear Algebra I
Extra Practice Problems
In each question, you answer by adding up the numbers of the correct statements. (For
example, if the statements are numbered 1, 2, 4, 8 and the rst three are correct, the answer
sh
DEPARTMENT OF MATHEMATICS, IIT Guwahati
MA101: Mathematics I, July - November 2014
Solutions of Tutorial Sheet: LA - 3
1. Check, without calculating the actual value, whether the determinant of the following matrix is even or odd:
2
5
2
1
2
3
5
3
5
2
7
9
2014-15 First Semester
MATH 2101 Linear Algebra I
Assignment 2
Due date: 10 Oct 2014 17:00
2 1
0
1
2 1 3
2 3 1
1. (Easy! ) Let A =
,B =
, C = 0 6 and D = 2
3 .
4 1 0
4 0 1
2 3
1 1
Find each of the following matrices if it is dened.
(a) (2)A
(b) A + 3B
(c)
2014-15 First Semester
MATH 2101 Linear Algebra I
Assignment 2 Solution
4 2 6
8 2 0
1. (a)
4 10 6
8 1 3
(b)
(c) It is undened as B and C are of dierent sizes.
(d) It is undened as BC and CB are of dierent sizes. BC is a 2 2 matrix while CB
is a 3 3 matrix
2014-15 First Semester
MATH 2101 Linear Algebra I
Assignment 3 Solution
1. (a) We have
x1
x2
x1 + x2
T y1 + y2 = T y1 + y2
z1
z2
z1 + z2
x1 + x 2
=
x1 + x 2 + y 1 + y 2
x1 + x2 + y1 + y2 + z1 + z2
x1
x2
= T y1 + T y2
z1
z2
and
ax
ax
x
2014-15 First Semester
MATH 2101 Linear Algebra I
Assignment 1 Solution
1. (Note: Try to use the same notation as the lecture notes or the textbook.While you can
perform several operations at once, you should not interchange rows and you should use
only o
2014-15 First Semester
MATH 2101 Linear Algebra I
Assignment 3
Due date: 31 Oct 2014 17:00
1. Determine whether each of the following is a linear transformation or not.
(a) T : R3 R3 , T (x, y, z)T ) = (x, x + y, x + y + z)T
(b) T : R3 R3 , T (x, y, z)T )
2014-15 First Semester
MATH 2101 Linear Algebra I
Assignment 5 Solution
1. (a) We rst compute the reduced row-echelon form of A (calling it B) to be
1 0 0 13
20
21
0 1 0 20
0 0 1 3
4
Since row operations do not change the row space, the row space of A a
2014-15 First Semester
MATH 2101 Linear Algebra I
Assignment 4
Due date: 14 Nov 2014 17:00
1. (Easy! ) In each of the following, compute det A and use the adjugate of A to nd A1
(if it exists).
(a) A =
1 2
0 1
(b) A =
1 2
0 0
(c) A =
1 2
3 4
1 1 1
(d) A =
2014-15 First Semester
MATH 2101 Linear Algebra I
Assignment 5
Due date: 28 Nov 2014 17:00
1. (Easy! ) In each of the following, nd a basis for the row space, the column space and the
null space of A.
(a)
1 3 2 1
A= 2 1 3 2
3 4 5 6
(b)
A=
2. Let S = cfw_
2014-15 First Semester
MATH 2101 Linear Algebra I
Assignment 4 Solution
1. (a) The determinant of A is 1(1) 0(2) = 1 and hence the inverse of A is
1
A
1 1 0
1
adjA =
=
det A
1 2 1
T
=
1 2
0 1
.
(b) Expanding along the second row, we see that det A = 0 and
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH 2101: LINEAR ALGEBRA I
9:30 am - 12:00 noon
23 Dec, 2014
Only approved calculators as announced by the Examinations Secretary can be used in this
examination. It is candidates' responsibility to e