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