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VED1
E L-LOVELY-H math22-1 IInd 6-8-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

noEPk;soh dk rfDs

B'N T[go'es ;kofDe dk fsZi/ ekbw d/ nXko s/ ft;Eko eoB s/

= x(x – 1) (x – 6) A = 1 {(0 – 1 (1 – x)} – 0 {0 – 2} + (1 – x) {(5 – x) (1 – x) – 4}
Gkt, i/eo x ≠ 0, 1 ns/ 6 w?fNqe; A dh o?Ae 3 j't/rh

5  − x 2 
ns/ i/eo x = 0, 1, 6 sK   =− 2 ≠ 0, o?Ae 2 j't/rh.
 1 0 
o/yh fBoGosk ns/ w?fNqe; dh o?Ae (Linear Dependance and Rank of Matrix)L fJZe w?fNqe;
dhnK gzeshnK (ekbw) ftZu sK jh o/yh fBoGosk d/yh iKdh j? id'A T[jBK gzeshnK (ekbw) dk
o/yh ;z:'iB Iho' t/eNo (vector) d/ pokpo j[zdh j?. Gktl

i/eo

fJZE/ K 1 , K 2 ns/ K 3 ftZu xZN s'A xZN fJZe dk w[Zb Iho' j'Dk ukjhdk j?.

T[dkjoD 1L fBZu/ fdZs/ j'J/ w?fNqe; dh o/yh ;[szsosk dh iKu eo' ns/ o?Ae eZY'l
 1 2 4

A =   2 4 8

  3 6 12 
jZb L r[Dk eoB s/ Row 1 (R 1 ) ns/ 2(R 2 ) ftZu ^1 ns/ i'VB s/ 3(R 3 )] sK

–1R 1 – 1 R 2 + R 3 = 0 (1)
–2 R 1 + R 2 = 0 (2)
–3 R 1 + R 3 = 0 (3)
;wheoD (1) ftZu R 1 , R 2 , ns/ R 3 ftZu o/yh ;[szsosk BjhA j?, ;wheoD (2) R 1 , ns/ R 2 ns/
;wheoD (3) R 1 ns/ R 3 ftZu o/yh fBoGosk do;k fojk j?. o?Ae d/ bJh,

 1 2 4  1 2 4



2 4 8 ∼   0 0 0 Gkt o?Ae (A) = 1 j't/rh.



  3 6 12    0 0 0  
 6 3 5 


T[dkjoD 2L i/eo A =− 10 2 8 sK o/yh fBoGosk dk gqhyD eo' ns/ w?fNqe; (A) dh


  5 2 3 
o?Ae eZY'.
jZb L C 1 R 1 + C 2 R 2 + C 3 R 3 = 0
6C 1 – 10C 2 + 5C 3 = 0 (1)
3C 1 + 2C 2 + 2C 3 = 0 (2)
5C 1 + 8C 2 + 3C 3 = 0 (3)

310 LOVELY PROFESSIONAL UNIVERSITY