TIFR-2011-Maths-A-3

Question

 Let $A$ be a $5 \times 5$ matrix with real entries, then $A$ has

• A. An eigenvalue which is purely imaginary
• B. At least one real eigenvalue
• C. At least two eigenvalues which are not real
• D. At least $2$ distinct real eigenvalues

Answer 1

In 5*5 matrix , there can be 5 eigen value

Now imaginary eigen values comes in pair

So,there can be maximum 2 pair of imaginary eigen values

So, atleast 1 real eigen value should be there

Answer will be (B)