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DETERMINANTSB. Com. III year
2016 - 17
Advance Business Mathematics
8584992992
03 (vi)
0 (v)
42 (iv)
(iii)
24 (ii)
51 (i)
Answers 1.
2hab
1 23
2 1 4
34 1
(vi)
211815
201714
191613
(v)
33 3
2 22
1 1 1
(iv)
(iii)
2 4
52 (ii)
97
34 (i)
: Evaluate 1.
bh
ha
2
DETERMINANTSB. Com. III year
2016 - 17
Advance Business Mathematics
8584992992
4abc (iii)
1 (ii)
1cb (i)
Answers 2.
222
zyx
a
0
654
543
432
(ii)
0
954
876
171210
(i)
that,prove expanding Without 3.
(iii)
1
1
1
(ii)
1
1
1
(i)
: sdeterminat following theof value theFind 2.
ccc
bbb
aaa
xy
xz
yz
cba
cba
cba
3
DETERMINANTSB. Com. III year
2016 - 17
Advance Business Mathematics
8584992992
]'(Hons.)B.Com.[C.U.
cbbaac
baaccb
accbba
ac
cb
ba
cac
bcb
aba
rcz
pax
qby
cba
rqp
zyx
rqp
zyx
cba
02 0 (vii)
1
1
1
1
1
1
(vi)
(v)
0
1
1
1
(iv)
0
0
0
0
(iii)
cba
bac
acb
cb
ca
ba
4
DETERMINANTSB. Com. III year
2016 - 17
Advance Business Mathematics
8584992992
]99')(....[92 9323232 (x)
]95')(....[639 11246 (ix)
]82')(....[138 ,232 ,03 (viii)
5213
,2621
,3432
(vii)
]89')(....[57432552 ,6535 (vi)
]05')(.....[823 ,632 ,932 (v)
]88')(....[423 ,12 ,12 (iv)
]90')(....[43 ,332 ,62 (iii)
42 ,523y (ii)
]01')(....[523 ,12 (i)
: method sCramer'by Solve 4.
H ComBU C zyx, zyx, zyx
H ComBU C cba, cba, cba
H ComBU C zyzyx zyx
zyxzyx
zyx
H Com BUC zx, zy yx
H Com BUBN zyxzy xzyx
H Com BUC zyxzy xzyx
H Com BUC zyxzy xzyx
y xx
H Com BUC yx yx
1,12 (iii)
32 (ii)
11 (i)
Answers 4.
z, yx
, yx
, yx
9,107 (vi)
18
5,
18
29
18
35 (v)
1,01 (iv)
z, yx
z, yx
z, yx
1,32 (x)
7,3
4
3
1 (ix)
3,11 (viii)
2,11 (vii)
z, yx
c, ba
z, yx
z, yx
5
DETERMINANTSB. Com. III year
2016 - 17
Advance Business Mathematics
8584992992
222
2
2
2
222
3
3
3
3
2
2
2
1
1
1
1
(vii)
111
111
111
(vi)
(v)
(iv)
1
1
1
(iii)
22
22
22
(ii)
1
1
1
(i)
: that Prove 5.
cba
cbcca
bcbab
acaba
xyzzxyzxy
z
y
x
cbaaccbba
baaccb
cba
cba
baxbxax
xba
bxa
bax
cba
baccc
bacbb
aacba
accbba
cc
bb
aa
6
[ C. U. B. Com. (Hons.) ’95 ]
[ C. U. B. Com. (Hons.) ’04 ]
[ C. U. B. Com. (Hons.) ’02 ]
[ C. U. B. Com. (Hons.) ’94 ]
DETERMINANTSB. Com. III year
2016 - 17
Advance Business Mathematics
8584992992
0
111
(ii) 0 (i)
that,show ,0 If 6.
333
222
zyx
zyx
yxxzzy
zyx
zyx
zyx
]RRby row 2 and RRby row 1 theReplace :[Hint
1
122
212
221
(xiii)
1111
111
1
1
1
(xii)
43321
83622
43321
(xi)
1
1
1
(x)
2
2
2
2
(ix)
1
1
1
(viii)
32nd31st
322
22
22
22
22
222
222
222222
23
23
23
3
22
22
22
ab
ba
baab
abaab
babba
c
c
b
b
a
acba
ba
ca
cb
yx
yyy
yyy
yxyxyx
wuvwuvuwwvvu
ww
vv
uu
cba
bacac
bacbc
bacba
baaccb
baba
acac
cbcb
7
[ C. U. B. Com. (Hons.) ’05 ]
[ C. U. B. Com. (Hons.) ’2000 ]
[ C. U. B. Com. (Hons.) ’91 ]
DETERMINANTSB. Com. III year
2016 - 17
Advance Business Mathematics
8584992992
323
165
432
(ii)
223
654
321
(i)
: tsdeterminan twofollowing theof tsdeterminan reciprocal and adjugate theFind .10
1 that,prove other, toequal and zero is of none and 0
1
1
1
If 9.
1
1
1
: squareperfect ist determinan following that theShow .8
Factorise 7.
32
32
32
2
2
2
2
2
2
xyz x, y, z
zzz
yyy
xxx
aa
aa
aa
ccab
bbca
aabc
12
1
2
1
12
736
5
6
1
36
19
2
3
1
9
4
31821
561
81216
(ii)
1213
4
3
7
3
23
7
3
10
3
2
;
363
472
7102
(i) : Answers 10.
; -
--
8
cabcabaccbba
Answers 7.
DETERMINANTSB. Com. III year
2016 - 17
Advance Business Mathematics
8584992992
322
22
22
222
4
0
0
0
that,show hence ;
0
0
0
Evaluate 11.
cba
babcca
bcacab
acabcb
ab
ac
bc
ab
ac
bc
22
22
22
33
33
22
11
2
2
2
:t determinan following theof value thefind hence ; ba
0
0
0
that Prove .13
?t determinan thisof value theist Wha
t.determinanorder thirda as
0
0
0
of square theExpress 12.
aabb
abba
baab
ab
ba
ba
ba
ba
ba
0 ;
Answers 12.
2
3
2
332323131
3232
2
2
2
22121
31312121
2
1
2
1
babbaabbaa
bbaababbaa
bbaabbaaba
233a
Answers 13.
b
abc2
Answers 11.
9
DETERMINANTSB. Com. III year
2016 - 17
Advance Business Mathematics
8584992992
0
0
0
evaluate otherwiseor hence; factorslinear ofproduct as ;
1
1
1
Express 14.
22
22
22
2
2
2
bcac
cbab
caba
cc
bb
aa
2333
222
222
222
333
3
thatprove hence ; 3 that Prove 15.
abccba
bcaabccab
cabbcaabc
abccabbca
abccba
acb
bac
cba
2222 ;
Answers 14.
accbbaaccbba
10
DETERMINANTSB. Com. III year
2016 - 17
Advance Business Mathematics
8584992992
0
,
Answers 17.
1 (ii)
, , (i)
Answers 16.
333
222
111
3232
3232
3232
3232
222
cba
cba
cba
abba
caacy
abba
bccbx
zyx
bcac
bacckkz
cbab
acbbkky
caba
cbaakkx
. and
of valuessame by the satisfied are 3 ,2 ,1 0 equations three the that
order thirdoft determinan a of form in thecondition thefind hence and 0
,0 ,0 : equations thesolve toRule sCramer' Use17.
]0 and unequal are ,,[
, ,3 (ii)
unequal] are ,,[ , ,1 (i)
: Rule sCramer'by Solve 16.
3232
333222
333333222222
2
yx
icybxa
abba
cybxacybxa
cabcabcba
cbazcybx acbazcybxazyx
cbakabzcaybcxkczbyaxzyx
iii
11
DETERMINANTSB. Com. III year
2016 - 17
Advance Business Mathematics
8584992992
kcfygxfbyhxghyax
k yx
cyx
zb
xz
ya
zy
x
zx, y
bxb
mmm
aax
xbac
axcb
cbxa
x
x
x
xbb
bxa
aax
,0 ,0
: of valueobtain the equations, following thefrom and Eliminate 20.
, ,
: equations following thefrom and Eliminate 19.
0 )v(i
0 )ii(i
0
24
24
24
i)i(
0 (i)
: Solve 18.
a, b
cabcabcba cba
baa, b,
(iv)
, (iii)
2,4 (ii)
(i)
Answers 18.
2
1222
2
2222
Answer 20.
hab
chbgaffghabc
12
Answer 19.
abccabcab
12
DETERMINANTSB. Com. III year
2016 - 17
Advance Business Mathematics
8584992992
The solutions of this set of exercise will be publishedon
Friday, 30-09-2016
Additional set of illustrations and problems will bePublished shortly.
Any error if found, please whatsapp (8584992992) for instantly correction .
13
DETERMINANTSB. Com. III year
2016 - 17
Advance Business Mathematics
8584992992
For Download Link
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14