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Ex 4.2, 15 - Let A be a square matrix of order 3 x 3, then |kA| - Ex 4.2

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  1. Chapter 4 Class 12 Determinants
  2. Serial order wise
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Ex4.2, 15 Choose the correct answer. Let A be a square matrix of order 3 × 3, then kA﷯ is equal to A. k A﷯ B. k2 A﷯ C. k3 A﷯ D. 3k A﷯ Let A = a1﷮b1﷮c1﷮a2﷮b2﷮c2﷮a3﷮b3﷮c3﷯﷯﷮3×3﷯ We need to find kA﷯ kA = k a1﷮b1﷮c1﷮a2﷮b2﷮c2﷮a3﷮b3﷮c3﷯﷯ = 𝐤a1﷮𝐤b1﷮𝐤c1﷮𝐤a2﷮𝐤b2﷮𝐤c2﷮𝐤a3﷮𝐤b3﷮𝐤c3﷯﷯ kA﷯ = ka1﷮kb1﷮kc1﷮ka2﷮kb2﷮kc2﷮ka3﷮kb3﷮kc3﷯﷯ Taking out k common from R1 R2 & R3 = k. k. k a1﷮b1﷮c1﷮a2﷮b2﷮c2﷮a3﷮b3﷮c3﷯﷯ = k3 a1﷮b1﷮c1﷮a2﷮b2﷮c2﷮a3﷮b3﷮c3﷯﷯ = k3 |A| Thus correct answer is C

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