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  1. Home
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Miscellaneous·2022·Easy

Consider the determinant Δ = | a₁₁ a₁₂ a₁₃ | | a₂₁ a₂₂ a₂₃ | | a₃₁ a₃₂ a₃₃ | If a₁₃ = yz, a₂₃ = zx, a₃₃ = xy and the minors of a₁₃, a₂₃, a₃₃ are respectively (z−y), (z−x),(y−x) then what is the value of Δ?

Consider the determinant Δ = | a₁₁ a₁₂ a₁₃ |
    | a₂₁ a₂₂ a₂₃ |
    | a₃₁ a₃₂ a₃₃ | If a₁₃ = yz, a₂₃ = zx, a₃₃ = xy and the minors of a₁₃, a₂₃, a₃₃ are respectively (z−y), (z−x),(y−x) then what is the value of Δ?

Options

  1. a.

    (z−y)(z−x)(y−x)

    Correct answer
  2. b.

    (x−y)(y−z)(x−z)

  3. c.

    (x−y)(z−x)(y−z)(x+y+z)

  4. d.

    (xy+yz+zx)(x+y+z)

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