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Ex 4.2, 2 - Using property of determinants - Class 12 CBSE - Whole row/column zero

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  1. Chapter 4 Class 12 Determinants
  2. Serial order wise
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Ex 4.2, 2 Using the property of determinants and without expanding, prove that: a−b﷮b−c﷮c−𝑎﷮b−c﷮c−a﷮a−b﷮c−a﷮a−b﷮b−c﷯﷯ = 0 a−b﷮b−c﷮c−𝑎﷮b−c﷮c−a﷮a−b﷮c−a﷮a−b﷮b−c﷯﷯ Making first row 0 by Applying R1 →R1 + R2 + R3 = a−b+b−c+c−a﷮b−c+c−a+a−b﷮c−a+a−b+b−c﷮b−c﷮c−a﷮a−b﷮c−a﷮a−b﷮b−c﷯﷯ = 0﷮0﷮0﷮b−c﷮c−a﷮a−b﷮c−a﷮a−b﷮b−c﷯﷯ = 0 c−a﷮a−b﷮a−b﷮b−c﷯﷯ – 0 b−c﷮a−b﷮c−a﷮b−c﷯﷯ + 0 b−c﷮c−a﷮c−a﷮a−b﷯﷯ = 0 – 0 + 0 = 0 = R.H.S Thus, L.H.S = R.H.S Hence proved

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