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Let A = open square brackets table row 0 cell 2 y end cell z row x y cell negative z end cell row x cell negative y end cell z end table close square brackets and A' . A = I, then the value of x to the power of 2 end exponent plus y to the power of 2 end exponent plus z to the power of 2 end exponent is -

  1. 1    
  2. 2    
  3. fraction numerator 1 over denominator 2 end fraction    
  4. None of these    

The correct answer is: 1


    I = A'A = open square brackets table row 0 x x row cell 2 y end cell y cell negative y end cell row z cell negative z end cell z end table close square brackets open square brackets table row 0 cell 2 y end cell z row x y cell negative z end cell row x cell negative y end cell z end table close square brackets
    = open square brackets table row cell 2 x to the power of 2 end exponent end cell 0 0 row 0 cell 6 y to the power of 2 end exponent end cell 0 row 0 0 cell 3 z to the power of 2 end exponent end cell end table close square brackets
    therefore 2x2 = 6y2 = 3z2 = 1
    therefore x to the power of 2 end exponent plus y to the power of 2 end exponent plus z to the power of 2 end exponent= fraction numerator 1 over denominator 2 end fraction plus fraction numerator 1 over denominator 6 end fraction plus fraction numerator 1 over denominator 3 end fraction equals fraction numerator 3 plus 1 plus 2 over denominator 6 end fraction equals 1

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