Old Exam Papers Dec. 2010 - Video

fl) dhft;s fd leqPp; G ? lA, B, C, Dq,
tgk¡
L
NM O QP L ?
NM O QP L ?
?
NM O QP 0 1
1 0
A ? B C D
L NMO QP ? 1 0 0 1 ? 1 0
, , ,
0 1 ? 1 0 0 ? 1
vkO;wg xq.ku ds fy, Øefofues; lewg gSA
(b) Prove that the intersection of any two subgroups of
a group G is also a subgroup of G.
fl) dhft;s fd fdlh lewg G ds fdUgha nks milewgksa
dk loZfu"V lewg G dk milewg gksrk gSA
1 2 3 4 5
2. (a) If p q
2 4 5 3 1
? F H G
prove that :
I,
? 2 3 4 KJ b g
cbgbgbg h
? 1
pqp ? p 2 p 3 p 4
1 2 3 4 5
;fn p q
2 4 5 3 1
? F H G
rks fl) dhft;s %
? 1
pqp ? p 2 p 3 p 4
I,
? 2 3 4 KJ b g
cbgbgbg h
600 2 MT-07
Papers (A) (December) 2010
(356)
fl) dhft;s fd QhYM F, fdlh Hkh F ds miQhYM
S ij lfn'k lef"V gSA
7. (a) If U (F) and W (F) are two subspaces of the vector
space V (F), then (U + W) (F) is also a subspace.
;fn U (F) rFkk W (F) lfn'k lef"V V (F) ds nks
milef"V gSa rks (U + W) (F) Hkh milef"V gksxkA fl)
dhft;sA
(b) Prove that vectors ba 1, a2g
and b 1, b2g? V2bg F are
linearly dependent if a1b2 ? a2b1 ? 0.
fl) dhft;s fd lfn'k a , a
b1 2g
rFkk b1 , b2 ? V2 F
,d?kkrr% ijrU= gS] ;fn a1b2 ? a2b1 ? 0
b g bg
8. (a) If x, y, z are L.I. vectors in a vector space V Fbg,
then prove that x ? y, x ? y, x ? 2 y ? z are also
linearly independent.
;fn x, y, z, V (F) ds lfn'k gks rFkk ,d?kkrr% LorU=
lfn'k gks] rks fl) dhft;s fd x ? y, x ? y, x ? 2 y ? z
Hkh ,d?kkrr% LorU= gksaxsA
(b) Prove that every finite dimensional vector space has
a basis.
MT-07 5 PTO