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Manipal MET2017MathematicsDeterminants

If ₁= | array lll x & a & b b & x & a a & b & x array | and ₂= | array ll x & b a & x array | are the given determinants, then

Options

  1. A₁=3 ( ₂ )^2
  2. B( d d x ) ( ₁ )=3 ₂
  3. C( d d x ) ( ₁ )=3 ( ₂ )^2
  4. D₁=3 ( ₂ )^ 3 / 2

Correct answer

B. ( d d x ) ( ₁ )=3 ₂

Step-by-step solution

aligned & Given, ₁= | array lll x & a & b b & x & a a & b & x array |, ₂= | array ll x & b a & x array | & aligned & d d x ( ₁ ) &= | array lll 1 & 0 & 0 b & x & a a & b & x array |+ | array lll x & a & b 0 & 1 & 0 a & b & x array |+ | array lll x & a & b b & x & a 0 & 0 & 1 array | & = | array ll x & a b & x array |+ | array ll x & b a & x array |+ | array ll x & a b & x array |=3 ₂ & d d x ( ₁ )=3 ₂ aligned aligned

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