Ex 4.5, 3 - Chapter 4 Class 12 Determinants

Transcript

Ex 4.5, 3 Verify A (adj A) = (adj A) A = 𝐴﷯ I . 2﷮3﷮−4﷮−6﷯﷯ Let A = 2﷮3﷮−4﷮−6﷯﷯ adj A = 2﷮3﷮−4﷮−6﷯﷯ = −6﷮−3﷮4﷮2﷯﷯ 𝐴﷯ = 2﷮3﷮−4﷮−6﷯﷯ = (2 × – 6 – 3 × – 4) = (– 12 + 12) = 0 Calculating A (adj A) = 2﷮3﷮−4﷮−6﷯﷯ −6﷮−3﷮4﷮2﷯﷯ = 2 × −6﷯+3 ×4﷮2 ×−3+3×2﷮−4 × −6﷯+(−6) ×4﷮−4 × −3﷯+(−6) ×2﷯﷯ = −12+12﷮−6+6﷮+ 24 −24﷮12−12﷯﷯ = 0﷮0﷮0﷮0﷯﷯ Similarly (adj A)A = −6﷮−3﷮4﷮2﷯﷯ 2﷮3﷮−4﷮−6﷯﷯ = − 6 2﷯+(−3) (−4)﷮−6 3﷯+ −3﷯(−6)﷮4 2﷯+2(−4)﷮4 3﷯+2 (−6)﷯﷯ = −12+12﷮−18+18﷮8 −8﷮12−12﷯﷯ = 0﷮0﷮0﷮0﷯﷯ Also |A| I = 0I = O ∴ A (adj A) = (adj A)A = |A|I Hence Proved