lkee1161 lkee1161
  • 15-01-2020
  • Mathematics
contestada

Suppose that λ is an eigenvalue of A. Show that 2λ is then an eigenvalue of 2A.

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afsahsaleem afsahsaleem
  • 15-01-2020

Answer:

Proof:

If λ is an eigenvalue of A then for some x≠0,

[tex]Ax=\lambda x\\\\Adding\,\,Ax\,\,on\,\,both\,\,sides\\\\Ax+Ax=\lambda x+Ax\\\\2Ax=\lambda x+\lambda x\\\\2Ax=2\lambda x[/tex]

Which shows that if λ is an eigenvalue of A, 2λ is then an eigenvalue of 2A.

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