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Question

If k . open square brackets table row cell negative 1 end cell 2 2 row 2 cell negative 1 end cell 2 row 2 2 cell negative 1 end cell end table close square brackets is an orthogonal matrix, then k is equal to-

  1. 1    
  2. 1/2    
  3. 1/3    
  4. None of these    

The correct answer is: 1/3


    Let A = k open square brackets table row cell negative 1 end cell 2 2 row 2 cell negative 1 end cell 2 row 2 2 cell negative 1 end cell end table close square brackets
    Since A is orthogonaltherefore AAT = I
    k2 open square brackets table row 9 0 0 row 0 9 0 row 0 0 9 end table close square brackets= Irightwards double arrow 9k2I = I rightwards double arrow k2 = fraction numerator 1 over denominator 9 end fractionrightwards double arrow k = ± fraction numerator 1 over denominator 3 end fraction

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