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 th
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
Q
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 n
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH2101 Linear Algebra I
Assignment 2
Due date: 24 Feb, 2017 before 18:00.
Please write down your name, university number and tutorial group numb
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH2101 Linear Algebra I
Tutorial 1
Date : Jan 23, 2017 Jan 27, 2017
1. Let
2 1 1
A = 3 0 2 ,
1 1 0
1 3 1
B= 0
1
2 .
2 3 4
Compute
(a) 2A B,
(b)
T3/MATH2014/2015-16/1st
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH2101 Linear Algebra I
Tutorial 3
Date : Feb 13, 2017 Feb 17, 2017
2 1
0
1
2 1 3
2 3 1
1. Let A =
, B =
, C = 0 6 and D
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH2101 Linear Algebra I
Assignment 1
Due date: 9 Feb, 2017 before 18:00
Please write down your name, university number and tutorial group number
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH2101 Linear Algebra I
Tutorial 2
Date : Feb 6, 2017 Feb 10, 2017
1. Determine whether w is a linear combination of u and v in each case.
" #
"
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH2101 Linear Algebra I
Tutorial 4
Date : Feb 20, 2017 Feb 25, 2017
1. In each of the following, find A1 by using row operations, or show that A
2017-18 Second 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 s
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH2101 Linear Algebra I
Tutorial 1
1. Let
y
x+y
x2
0
z .
A= 0
y + 6 2z 1 y z
Find the values of x, y and z such that A is a symmetric matrix.
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH2101 Linear Algebra I
Tutorial 1 Solutions
1. The matrix A is symmetric if and only if A = AT . This is equivalent to
x + y = 0,
x2 = y + 6,
z
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 sh
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 1
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
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.
An
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
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 fo
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 fol
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 die
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 + z
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, yo
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 )
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 opera
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
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.
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) Ex
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
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 numbere