Ex 4.5, 3 - Chapter 4 Class 12 Determinants (Term 1)

Transcript

Ex 4.5, 3 Verify A (adj A) = (adj A) A = |𝐴| I, where A = [■8(2&[email protected]−4&−6)] Let A = [■8(2&[email protected]−4&−6)] adj A = [■8(2&[email protected]−4&−6)] = [■8(−6&−[email protected]&2)] |𝐴| = |■8(2&[email protected]−4&−6)| = 2 × (–6) – 3 × (–4) = –12 + 12 = 0 Calculating A (adj A) = [■8(2&[email protected]−4&−6)] [■8(−6&−[email protected]&2)] = [■8(2 ×(−6)+3 ×4&2 ×−3+3×[email protected]−4 ×(−6)+(−6) ×4&−4 ×(−3)+(−6) ×2)] = [■8(−12+12&−[email protected]+ 24 −24&12−12)] = [■8(0&[email protected]&0)] Similarly (adj A)A = [■8(−6&−[email protected]&2)] [■8(2&[email protected]−4&−6)] = [■8(− 6(2)+(−3) (−4)&−6(3)+(−3)(−6)@4(2)+2(−4)&4 (3)+2 (−6))] = [■8(−12+12&−[email protected] − 8&12−12)] = [■8(0&[email protected]&0)] Also |A| I = 0I = O ∴ A (adj A) = (adj A)A = |A|I Hence Proved