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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. 1/3    
  3. ½    
  4. none of these    

The correct answer is: 1/3


    since A is orthogonal therefore AAT = I
    rightwards double arrow kopen square brackets table attributes columnalign center center center columnspacing 1em end attributes 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 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 = I
    rightwards double arrow k2open square brackets table row 9 0 0 row 0 9 0 row 0 0 9 end table close square brackets = I
    rightwards double arrow 9k2I = I rightwards double arrow k = ± 1/3

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