RKS Rathore
Linear Algebra and Applied Matrix Theory
Lecture Notes in
Linear Algebra and Applied Matrix Theory
by
RKS Rathore
(Ph.D. IIT Delhi, D.Sc. Delft University, The Netherlands)
Professor, Department of Mathematics, IIT Kanpur
For: MTH 201, MTH 310
I C.S.EMnins 2008
MATHEMATICS
Mnxi11111111 M 11rks: 3f/O
"/1me 1'11/tJII'ed: 3 lltlitrS
om
Candidates should attempt Question Nos. I nnd S 11i1ich are compolsmy. and any three of the remainrng
quesuons seleeting ru leas~ one quesuon from each section.
PA
C. S. ( ~v1 ;\.I N)
EX~\1.,
2009
CDTNJNUA
Sl. No .
MATHEMATICS
PaperI
Th~ee
Time AllO\"ecl
H ours
I I Ma."Ximum
l.   
.,
Marks :

_ _J
INSTRUCTIONS
Each qu estion is printe d both tn
in English.
Answers must b e written zn
specified in the Admis

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C. S. cfw_ivlain Exam : 2011
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Serial No. (
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.l\IATHEMATICS.
Pap erI
(Time Allo wed. " Three Hou rs)
[Ma ximu m Mar ks : 300J
INSTRUCTIONS
Each question is printed both in Hindi and in Engl ish
Answers
C.S .E. (M AIN )
MA TH EM AT ICS 20 04
(PA PE RI I)
Tim e allo wed : 3 hour s
Max . Mar ks: 300
om
INS TRU CTI ONS
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Eac h ques tion is prin ted both in Hin di and in English.
Ans wer s mus t be writ ten in the med ium spec ified in the
A
C.S.E . (MAI N)
MAT HEM ATIC S200 4
(PAP ERI)
Time allowed : 3 hours
om
Max. Marks: 300
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INSTR UCTIO NS
Each question is printed both in Hindi and in English.
Answer s must be written in the medium specifi ed in the
Admission Certificate
CS cfw_MAIN) EXAM, 2010
Sl. No.
127
CDTNKNUA
MATHEMATICS
Paper
I
Time Allowed
Three Hours
I
I
j Maximum
Marks 300
INSTRUCTIONS
Each question is printed both in Hindi and
in English.
Answers must be written in the medium
specified in the Admission Certi
'
C.S.E. (MAIN)
M A TH EM A TI CS  2005
PAPERI
Time allowed : 3 hou rs
om
Ma xim um MarkS : 300
.e
xa
m
ra
ce
.c
INSTRUCfiONS
Eac h question is prin ted both in Hin di and in English
.
Answers mus t be written in the med ium spe cifi ed in the
Admission
C.S.E. (MAIN)
MATHEMATICS
2006
PAPERI
Time all ow ed: 3 hou rs
Maximum Marks : 300
INSTRUCTIONS
xa
m
ra
ce
.c
om
Ea ch question is pri nte d both in Hindi and in Eng
lish.
An swe rs mu st be written in the me diu m spe cifi ed in
the Admis'sion Certifica
SEC fiON 'A'
Q. l. Ans wer any five of the follo wing :
(a) If M and N are normal subgroups of a group G such that M
n N = cfw_e, show that every elem ent of M commutes with every
12
element ofN .
(b) Show that (1 + i) is a prime element in the ring R of
SEC TIO N'A!
Q. 1. Answer any five of the following:
(a) L~t S be the set of all real numbers except 1. Define * on S
by
1
xl/2 (1x )l/2
12
m
I
dx
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ce
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om
a* b =a +b + ab
Is (S, *) a group ?
Find the solution of the equation
12
2 * x * 3 = 7 inS.
(b
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s
.It
l2
FDTNMNUIA
MATHEMATICS
Paper1
I Time
Allowed : Three Hours
I
IMaximum Marks
300
I
INSTRUCTIONS
Each question is printed both in Hindi and in English.
Answers must be written in the medium specified in the
Admission Ce
Time Allowed: 3 hours
Maximum Marks: 300
.
om
Candidates should attempt Question Nos. 1 and 5 which are compulsory, and any three of the remaining
questions selecting at least one question from each section.
'(
SectionA
.c
Attempt any five of the follow