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AP EAMCET2003MathematicsDeterminants

If | array ccc (A+B) & - (A+B) & 2 B A & A & B - A & A & B array |=0 then B is equal to

Options

  1. A(2 n+1) 2
  2. B(2 n+1)
  3. Cn
  4. D2 n

Correct answer

A. (2 n+1) 2

Step-by-step solution

We have, | 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+ A B]+ 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 1+2 ^2 B-1=0 ^2 B=0 ^2 B= ^2 2 B=n 2 = 2 (2 n 1) B= 2 (2 n+1)

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