Mathematics Exam  >  Mathematics Questions  >  Considerthena)A has no real eigen valuesb)A h... Start Learning for Free
Consider   then
  • a)
     A has no real eigen values
  • b)
     A has only positive real eigen values
  • c)
     A has only negative real eigen values
  • d)
     A has both positive and negative real eigen values
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Considerthena)A has no real eigen valuesb)A has only positive real eig...
Clearly. A is a symmetric matrix. Also we know that eigen values ofasymmetric matrix are always real
⇒ Eigen values of A are real
Now Trace (A) =0 = sum of all eigen values.
⇒ A has both positive and negative eigen values
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Considerthena)A has no real eigen valuesb)A has only positive real eigen valuesc)A has only negative real eigen valuesd)A has both positive and negative real eigen valuesCorrect answer is option 'D'. Can you explain this answer?
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