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Question

If A = open square brackets table row 2 cell – 1 end cell row cell – 1 end cell 2 end table close square brackets and A2 – 4A – n I = 0, then n is equal to

  1. fraction numerator 1 over denominator 3 end fraction    
  2. – fraction numerator 1 over denominator 3 end fraction    
  3. – 3    
  4. 3    

The correct answer is: – 3


    open vertical bar table row cell 2 – lambda end cell cell – 1 end cell row cell – 1 end cell cell 2 – lambda end cell end table close vertical bar = 0
    4 + lambda squared – 4lambda  – 1 = 0
    lambda squared– 4lambda  + 3 = 0
    A2 – 4A + 3I = 0
    –n = 3 & n = – 3

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