Old Exam Papers June 2012 (Set 2)

;fn V fdlh {ks= F ij lfn'k lef"V vkSj
S bv 1, v2 ,.... vng bldk vk/kkj gS rks iznf'kZr dhft;s
fd V ds fdlh mileqPp; esa tks ,d ?kkrr% Lora= gS n
ls T;knk vo;o ugha gks ldrs gSaA
10. (a) If U and W be two sub-spaces of V (F) then show
that U W l u w / u U , w Wq
is the
smallest sub-space of V (F) which contain U W .
;fn U vkSj W fdlh lfn'k lef"V V (F) dh nks
milef"V;k¡ gksa rks iznf'kZr dhft;s fd
U W l u w / u U , w Wq,
V (F) dh
U W dks vUrfoZ"V djus okyh lcls NksVh milef"V
gSA
b g
mb 0, 0,
g r is a sub-space of V Rbg. Then
(b) If V ma , b, c a, b, c Rr
is a vector space and
W c c R
find dimensions of quotient space V
W .
b g
;fn V ma , b, c a, b, c Rr
,d lfn'k lef"V gS
vkSj W mb 0, 0,
cgc Rr,
V Rbg dh ,d milef"V
gS rks foHkkx lef"V V
W
dh foek Kkr dhft;sA
600 8 MT-07
A
MT-07
B.A./B.Sc. (Part III) EXAMINATION,
June, 2012
MATHEMATICS
Paper-MT-07
(Algebra)
Time allowed : Three hours
Maximum marks : 67
Attempt any five questions. Each
question carries equal marks.
fdUgha ik¡p iz'uksa ds mÙkj nhft;sA lHkh iz'uksa
ds vad leku gSaA
1. (a) Show that the group G l0 , 1, 2, 3, 4q
operation 5 is a Abelian Group where 5 is defined as follows :
a b
5
R
S
T
a b, if a b 5
a b 5, if a b 5
PTO