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Ex 4.2, 3 - Prove using property |2 7 65 3 8 75 5 9 86| = 0 - Ex 4.2

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  1. Chapter 4 Class 12 Determinants
  2. Serial order wise
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Ex 4.2, 3 Using the property of determinants and without expanding, prove that: 2﷮7﷮65﷮3﷮8﷮75﷮5﷮9﷮86﷯﷯ = 0 2﷮7﷮65﷮3﷮8﷮75﷮5﷮9﷮86﷯﷯ Applying C3 → C1 = 2﷮7﷮65−2﷮3﷮8﷮75−3﷮5﷮9﷮86−5﷯﷯ = 2﷮7﷮63﷮3﷮8﷮72﷮5﷮9﷮81﷯﷯ = 2﷮7﷮𝟗×7﷮3﷮8﷮𝟗×8﷮5﷮9﷮𝟗×9﷯﷯ Taking out 9 common from C3 = 9 2﷮7﷮7﷮3﷮8﷮8﷮5﷮9﷮9﷯﷯ Here, R2 & R3 are identical = 9 × 0 = 0 Thus, 2﷮7﷮65﷮3﷮8﷮75﷮5﷮9﷮86﷯﷯ = 0 Hence proved

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