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VED1
E L-LOVELY-H math19-1 IInd 6-8-11 IIIrd 24-1-12 IVth 21-4-12 VIth 10-9-12

noEPk;soh dk rfDs

-1
B'N fNZgDh^(i) i/eo A, B, C,....,AM ;wkB eqw d/ T[bN w?fNqe; jB, T[d'A (A.B.C.....M) = M
-1
-1
-1
....C B A
(ii) i/eo A fB:fws tor^w?fNqe; j?, T[d'A AB = 0 ⇒ B = 0;
i/eo B fB:fws tor^w?fNqe; j?, T[d'A AB = 0 ⇒ A = 0
(iii) w?fNqe; ftZu gfotos ns/ T[bN fefonk eqw ftfBw/: (Commutative) j?.

( )A′ − 1 = (A − 11
).
19H5 bzpe w?fNqe; (Orthogonal Matrix)

′
i/eo AA = I sK A B{z bzpe w?fNqe; efjzd/ jB.
n;t?fJS[Ze Involuntary w?fNqe;
2
i/eo A tor w?fNqe; j? ns/ A = I (ss;we iK fJekJh), sK A B{z n;t?fJS[Ze (Involuntary)
w?fNqe; efjzd/ jB.
T[dkjoD L do;kU fe fBwBfbus o{g d/ 2 % 2 w?fNqe;K d/ bJh r[DB eqw^ftfBw/:
jB^

jZb L fJZE/

ns/

;t?^w[bKeD (Self Assessment)

fBwBfbys eEBK ftZu'A ;Zu iK M{m dh gfjukD eo'
(State whether the following statements are True or False)^

6H t:{j A d/ ;zxNeK a ij d/ ;fj^yzvK C ji Bkb gqfs;Ekfgs eoe/ t:{j dk gfotos pDk
b?Ad/ jB. fJ; soQK pD/ gfotofss t:{j B{z A dk ;fjyzvi efjzd/ jB.
7H fe;h T[bN w?fNqe; dk ftgohs ftbZyD BjhA j[zdk j?.

8H i/eo B fB:fws tor w?fNqe; j?, T[d'A AB = 0 ⇒ A = 0
′
I
9H i/eo AA = sK A B{z Iho' w?fNqe; efjzd/ jB.
2
10H i/eo tor w?fNqe; A j? ns/ A = I, sK A B{z n;t?fJS[Ze w?fNqe; efjzd/ jB.

19H6 ;koKP (Summary)
• i/eo A fJZe m × n eqw dk w?fNqe; j?, T[d'A fJ;dhnK gzeshnK ns/ ;szGK B{z nkg;
ftZu pdbD Bkb fijV/ n × m w?fNqe; gqkgs j't/rk, T[;B{z A dk gfotos ejKr/ ns/
T
t
A′ iK A iK A Bkb do;ktKr/.
• w?fNqe; A ns/ B r[DB d/ bJh nB[ebB jB, sK AB dk gfotos T[seqw ftZu
gfotosK d/ r[DBcb d/ pokpo j't/rk Gkt i/eo A ns/ B eqw nB[;ko m × n ns/
n×p eqw d/ jB, T[d'A ( )AB ′ = ′ . B A′ H

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