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MHT CET20239 May 2023Evening ShiftMathematicsDeterminantsActual

If | array ccc (A+B) & - (A+B) & (2 B) A & A & B - A & A & B array |=0 , then the value of B is

Options

  1. An , n Z
  2. B(2 n +1) 2 , n Z
  3. C(2 n+1) 4 , n Z
  4. D2 n 3 , n Z

Correct answer

B. (2 n +1) 2 , n Z

Step-by-step solution

aligned & | array ccc (A+B) & - (A+B) & (2 B) A & A & B - A & A & B array |=0 & ( A + B )[( A B - A B )] & + (A+B)[ A B+ B A] & + 2 ~B [ ^2 ~A + ^2 ~A ]=0 & ( A + B ) ( A + B ) & + (A+B) (A+B)+ 2 B=0 & ^2(A+B)+ ^2(A+B)+ 2 B=0 & 1+ 2 B=0 & 2 ^2 ~B =0 & B =0 & B=(2 n+1) 2 for (n Z) & aligned

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