determinants problems b. com. iii year

DETERMINANTSB. Com. III year

2016 - 17

Advance Business Mathematics

8584992992

1


2016 - 17


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


2016 - 17


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


2016 - 17


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


2016 - 17


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


2016 - 17


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

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2016 - 17


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

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2016 - 17


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.


2016 - 17


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


2016 - 17


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


2016 - 17


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


2016 - 17


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


2016 - 17


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


2016 - 17


8584992992

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determinants problems b. com. iii year

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