Page 278 - DECO403_MATHEMATICS_FOR_ECONOMISTS_PUNJABI

VED1
E L-LOVELY-H math18-1 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 2H w?fNqe;K d/ ;ws[b ;zpzX (Equivalence Relations of Matrices)
i/eo A, B, C w?fNqe; nB[e[bB (Conformable) jB Gkt ;wkB eqw (Order) j?l sK

(i) A = A; ;ws[b ;zpzX (Reflexive Relation)
(ii) A = B ⇔ B = A ⇒ ;wfws ;zpzX (Symmetric Relations)
(iii) A = B ns/ B = C ⇒ A = C; ;zeqkwe ;zpzX (Transitive Relation)
fiZE/, ;ze/s (Notation) ⇒ i/eo HHHH sK (If....then) ns/ ⇔ i/eo ns/ e/tb i/eo (iff = if
and only if)
(T) A = A dk noE j? a ij = a ij fiZE/ i = 1, 2, 3, ....m ns/ j = 1, 2, 3, ....., n. fJZe ;t?s[b
;zpzX ejkT[Adk j?.
(n) A = [a ij ] m×n ns/ B = [b ij ] m×n jB sK A = B dk noE j? a ij = b ij iK b ij = a ij . fJ;
bJh bJh B = A.

∴ A = B ⇒ B = A fJ;B{z ;wfws ;zpzX efjzd/ jB.
(J) i/eo A = B, fJ;B{z B= C ;wfws ;zpzX efjzd/ jB^
a ij = b ij ns/ b ij = c ij

fJ; soQK a ij = c ij ∴ A = C
w?fNqe;K A, B, C ftZu T[j ;zpzX j?, fijV/ ;t?s[b, ;wfws ns/ ;zeqkwe j't/, s[bsk ;zpzX
ejkT[Adk j?. T[dkjoD ti'A^

s[b w?fNqe; dh gfoGkPk d[nkok x, y ns/ z dk wkB

fJ; soQK d' s[b w?fNqe;K d/ ;zrs ;zxNe s[b j[zd/ jB.
∴ x + 3 = 0; 2y + x = –7; z – 1 = 3 ns/ 4a – 6 = 2a
fJBQK ;wheoDK d[nkok x =–3; y = –2; z = 4 ns/ a = 3H

18H5 t:{jK dk :'r ns/ nzso (Addition and Subtraction of Matrices)

i/eo A = [a ij ] ns/ B = [b ij ] d' m × n eqw d/ w?fNqe; jB, T[d'A T[jBK dk :'rcb A + B n;hA
eqw m × n w?fNqe; C = [c ij ] d[nkok do;kT[Ad/ jB.
fiZE/ c ij = b ij , i = 1, 2, ......, m; j = 1, 2, ......., n ;ko/ wkBK d/ bJh.
fJZE/ fJj T[by:'r j? fe i/eo w?fNqe; ;wkB eqw d/ BjhA jB sK T[jBK dk :'rcb ;zGt
BjhA j?.
T[dkjoD 1H wkB eZY' (Evaluate)^

272 LOVELY PROFESSIONAL UNIVERSITY