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NDA2021MathematicsDeterminantsActual

If = | array lll a & b & c d & e & f g & h & i array | then what is | array ccc 3 d+5 g & 4 a+7 g & 6 g 3 e+5 h & 4 b+7 h & 6 h 3 f+5 i & 4 c+7 i & 6 i array | equal to?

Options

  1. A7
  2. B72
  3. C-72

Correct answer

3

Step-by-step solution

aligned & | array ccc 3 d+5 g & 4 a+7 g & 6 g 3 e+5 h & 4 b+7 h & 6 h 3 f+5 i & 4 c+7 i & 6 i array | & =6 | array lll 3 d+5 g & 4 a+7 g & g 3 e+5 h & 4 b+7 h & h 3 f+5 i & 4 c+7 i & i array | & Apply c₁ c₁-5 c₃ and c₂ c₂-7 c₃ & =6 | array lll 3 d & 4 a & g 3 e & 4 b & h 3 f & 4 c & i array |=72 | array lll d & a & g e & b & h f & c & i array | & =-72 | array lll a & d & g b & e & h c & f & i array | & =-7 q [ | ~A |= | A ^ | ] . aligned

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