Question

if 3 is an eigen value of matrix A then prove that 3+k is an eigen value of matrix A+kI​

Answer 1

Answer:

The converse is easy to show by multiplying Ax on the left by A (x is a eigenvector): AAx=A(λx)=λAx=λ2x but I was wondering if the converse is true. The same approach doesn't work to prove what I want, I think this shouldn't be true but I'm not so sure, any hints?