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If a₁, a₂, a₃, , a ₉ are in GP, then what is the value of the following determinant? | array lll a₁ & a₂ & a₃ a₄ & a₅ & a₆ a₇ & a₈ & a₉ array |

Options

  1. A0
  2. B1
  3. C2
  4. D4

Correct answer

A. 0

Step-by-step solution

As a₁, a₂, a₃ a₉ are in G.P. a₄ a₁ = a₅ a₂ = a₆ a₃ . .=r^3 ( where r= common ratio) Now, | array lll a₁ & a₂ & a₃ a₄ & a₅ & a₆ a₇ & a₈ & a₉ array |= | array ccc a₄- a₁ & a₅- a₂ & a₆- a₃ a₇- a₄ & a₈- a₅ & a₉- a₆ a₇ & a₈ & a₉ array | (Applying R₁ R₂-R₁ and R₂ R₃-R₂ ) = | array lll a₄ a₁ & a₅ a₂ & a₆ a₃ a₇ a₄ & a₈ a₅ & a₉ a₆ a₇ & a₈ & a₉ array |= | array lll r^3 & r^3 & r^3 r^3 & r^3 & r^3 a₇ & a₈ & a₉ array |=0

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