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  1. Chapter 4 Class 12 Determinants
  2. Serial order wise

Transcript

Ex 4.5, 3 Verify A (adj A) = (adj A) A = |๐ด| I, where A = [โ– 8(2&3@โˆ’4&โˆ’6)] Let A = [โ– 8(2&3@โˆ’4&โˆ’6)] adj A = [โ– 8(2&3@โˆ’4&โˆ’6)] = [โ– 8(โˆ’6&โˆ’3@4&2)] |๐ด| = |โ– 8(2&3@โˆ’4&โˆ’6)| = 2 ร— (โ€“6) โ€“ 3 ร— (โ€“4) = โ€“12 + 12 = 0 Calculating A (adj A) = [โ– 8(2&3@โˆ’4&โˆ’6)] [โ– 8(โˆ’6&โˆ’3@4&2)] = [โ– 8(2 ร—(โˆ’6)+3 ร—4&2 ร—โˆ’3+3ร—2@โˆ’4 ร—(โˆ’6)+(โˆ’6) ร—4&โˆ’4 ร—(โˆ’3)+(โˆ’6) ร—2)] = [โ– 8(โˆ’12+12&โˆ’6+6@+ 24 โˆ’24&12โˆ’12)] = [โ– 8(0&0@0&0)] Similarly (adj A)A = [โ– 8(โˆ’6&โˆ’3@4&2)] [โ– 8(2&3@โˆ’4&โˆ’6)] = [โ– 8(โˆ’ 6(2)+(โˆ’3) (โˆ’4)&โˆ’6(3)+(โˆ’3)(โˆ’6)@4(2)+2(โˆ’4)&4 (3)+2 (โˆ’6))] = [โ– 8(โˆ’12+12&โˆ’18+18@8 โˆ’ 8&12โˆ’12)] = [โ– 8(0&0@0&0)] Also |A| I = 0I = O โˆด A (adj A) = (adj A)A = |A|I Hence Proved

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.