Ex 4.1, 3 - Show that |2A| = 4|A|, if A = [1 2 4 2] - Ex 4.1

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  1. Chapter 4 Class 12 Determinants
  2. Serial order wise
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Ex 4.1, 3 If A = 1﷮2﷮4﷮2﷯﷯ , then show that 2A﷯ = 4 A﷯ We need to prove 2A﷯ = 4 A﷯ Taking L.H.S 2A﷯ First calculating 2 A 2A = 2 1﷮2﷮4﷮2﷯﷯ = 2×1﷮2×2﷮ 2×4﷮2×2﷯﷯ = 2﷮4﷮8﷮4﷯﷯ So, 2 A﷯ = 2﷮4﷮8﷮4﷯﷯ = 2(4) – 8 (4) = 8 – 32 = –24 Taking R.H.S 4 A﷯ As A = 1﷮2﷮4﷮2﷯﷯ So A﷯ = 1﷮2﷮4﷮2﷯﷯ = 1 (2) – 4 (2) = 2 – 8 = – 6 Hence, 4 A﷯ = 4 (2) = −24 = L.H.S ∴ L.H.S = R.H.S Hence proved

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