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Easy

Question

If M =open square brackets table row 1 2 row 2 3 end table close square bracketsand M2 lambdaM – straight I subscript 2 = 0, then lambda equals -

  1. –2    
  2. 2    
  3. –4    
  4. 4    

The correct answer is: 4


    We are given the matrix M and an equation for λ and asked to find the value of λ
    M space equals open square brackets table row 1 2 row 2 3 end table close square brackets
M squared equals open square brackets table row 1 2 row 2 3 end table close square brackets open square brackets table row 1 2 row 2 3 end table close square brackets equals open square brackets table row 5 8 row 8 13 end table close square brackets
M squared minus lambda M minus I space equals space 0
open square brackets table row cell 5 minus lambda minus 1 end cell cell 8 minus 2 lambda end cell row cell 8 minus 2 lambda end cell cell 13 minus 3 lambda minus 1 end cell end table close square brackets equals open square brackets table row 0 0 row 0 0 end table close square brackets
8 minus 2 lambda equals 0
lambda equals 4

    Therefore the correct option is choice 4

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