Page 277 - DECO403_MATHEMATICS_FOR_ECONOMISTS_PUNJABI

VED1
E L-LOVELY-H math18-1 IInd 21-10-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

fJekJh^18 L t:{j (w?fNqe;) L noE ns/ gqeko

T[go'es t:{j B{z w?fNqae; fteoD :'r = a + b + c j?. tor w?fNqe; A eqw, n × n ftZu w?fNqe; B'N
n
fteoD :'r & ∑ a j?. fiZE/, j = i efjzd/ jB ns/ T[;B{z Tr fbyd/ jB.
ij
i= 1
[XI] ;wfws w?fNqe; (Symmetric Matrix)
th
T[j tor w?fNqe; A (eqw n × n), fi;d/ jo/e (i – j) xNe (;zxNe) d/ bJh a ij = a ji j't/,
;wfws w?fNqe; ejkT[Adk j?, T[dkjoD ti'A,

T[go'es w?fNqe; fJZe ;wfws w?fNqe; j? feT[Afe a ij = a ji i.e. a 21 = h = a 12 ; a 32 = f = a 23 ; a 22 = b =
a 22
[XII] NKe^;wfws w?fNqe; (Skew-Symmetric Matrix)
th
T[j tor w?fNqe; A (eqw n × n), fi;d/ jo/e (i - j) fiBQK d/ jo/e oue d/ bJh a ji = a ij j't/,
NKe^;wfws w?fNqe; ejkT[Adk j?. T[dkjoD ti'A,

fteoD ;zxNeK a 11 , a 22 , a 33 , ........, a ij fJ; soQK j? ns/ gqshpzX a ij = – a ji d/ ;ko/ wkBK d/ bJh.
∴ 2a ij = 0 or – a ij = 0
fJ; bJh NKe^;wfws w?fNqe; d/ ;ko/ fteoD ;zxNe Iho' j[zd/ jB.

;t?^w[bKeD (Self Assessment)

ykbh ;EkBK dh g{osh eo' (Fill in the blanks)^
1H fJZe nkfJskeko nze nkfJs, fi;B{z gzeshnK ns/ ;szGK ftZu ftt;fEs ehsk frnk j't/
HHHHHHHHHHHHH ejkT[Adk j?.

2H i/eo fe;h th w?fNqe; ftZu gzeshnK ns/ ;szGK dh ;zfynk m ns/ n j'D, sK nkfJseko
nfGnk; ftZu e[ZbQ HHHHHHHHHHHHH ;zxNeK dh ;zfynk j't/rh.
3H i/eo fe;h w?fNqe; ftZu gzeshnK ns/ ;szGK dh ;zfynk pokpo j? sK T[;B{z HHHHHHHHHHHH
w?fNqe; efjzd/ jB.
4H i/eo fe;h w?fNqe; d/ ;ko/ ;zxNe Iho' j'D, sK T[j HHHHHHHHHHHH w?fNqe; ejkT[Adk j?.
5H i/eo fe;h B{z w?fNqe; d/ gqw[Zy fteoD T[Zs/ ;fEo ;zxNeK B{z SZv e/ pkoh ;G Iho' jB,
T[d'A T[;B{z HHHHHHHHHHHHH w?fNqe; efjzd/ jB.

18H4 w?fNqe; d/ w[Zy r[D (Important Properties of Matrices)

1H t:{jK dh ;wkBsk (Equality of Matrix)
d' w?fNqe; A = [a ij ] m×n , B = [b ij ] p×q s[b j'Dr/ i/eo d'jK d/ eqw (Order) pokpo j'Dr/ Gkt m = p;
n = q ns/ a ij = b ij j[zd/ jB.

LOVELY PROFESSIONAL UNIVERSITY 271