Check sibling questions

Ex 4.5, 3 - Verify A (adj A) = (adj A) A = AI [2 3 -4 -6]

Ex 4.5, 3 - Chapter 4 Class 12 Determinants - Part 2
Ex 4.5, 3 - Chapter 4 Class 12 Determinants - Part 3

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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

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.