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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 Pavitar Parkash Singh, Lovely Professional University

B'N fJekJh^22L nkt:{j (w?fNqe;) dh o?Ae

(Rank of Matrix)

ftP/ t;s{ (Contents)
T[d/P (Objectives)
gq;sktBk (Introduction)

22H1 o?Ae d/ r[D (Characteristics of Rank)
22H2 ;koKP (Summary)

22H3 Ppde'P (Keywords)
22H4 nfGnk; gqPB (Review Questions)
22H5 ;zdoG g[;seK (Further Readings)

T[d/P (Objectives)

fJ; fJekJh d/ nfXn?B s'A pknd ftfdnkoEh :'r j'Dr/L

• o?Ae d/ r[DK s'A ikD{ j'Dr/.
• o?Ae d/ r[DK B{z T[dkjoD ;fjs ;wMDr/.

gq;sktBk (Introduction)

w?fNqae; d/ Bkb ;zpzX oZyD tkbh fJZe wjZstg{oD ;zfynk B{z o?Ae efjzd/ jB. fJZe m × n
w?fNqe; A ftZu n ;szG t?eNo ns/ m xNe j?, sK o/ye ;[szso ;?N d/ tZX s'A tZX ;szG t?eNo
B{z T[; w?fNqe; dh o?Ae efjzd/ jB fJ;B{z r(A) d[nkok gqdofPs eod/ jB.

d{i/ PpdK ftZu fJj th efj ;ed/ jK fe ;[szso ;szGK dh tZX s'A tZX ;zfynk B{z w?fNqae; dh o?Ae
efjzd/ jB fJZe An × n w?fNqe; r?o fJZetuBh (non-singuler) T[d'A j[zdk j? id'A T[;dh o?Ae n d/
pokpo j't/rh.

22H1 o?Ad d/ r[D (Characteristics of Rank)

• e/tb Iho' w?fNqe; dh jh Iho' o?Ae j[zdh j?.
• rank (A) ≤ min (m, n) {o?Ae (A) ≤ fBT{Bsw (m, n)}

• i/eo A tor w?fNqe; j? (m = n) sK A sK jh gfotosh j't/rk id'A A dh o?Ae n
j't/rh.
• o?Ae (AB) ≤ fBT{Bsw (o?Ae A, o?Ae B)

• o?Ae (A) O o?Ae (B) – n ≤ o?Ae (AB)
• o?Ae (CA) & o?Ae (A) {C ;fEo nze j?}

eh s[;hA ikDd/ j' ;[szso gzeshnK dh tZX s'A tZX ;zfynk B{z nkt:{j (w?fNqe;) dh o?Ae
efjzd/ jB.

308 LOVELY PROFESSIONAL UNIVERSITY