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mlarson9000
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Homework Statement
Let A be an nxn matrix and let I be the nxn identity matrix. Compare the eigenvectors and eigenvalues of A with those of A+rI for a scalar r.
Homework Equations
The Attempt at a Solution
I think I should be doing something like this:
det(A-[tex]\lambda[/tex]I), and
det((A+rI)-[tex]\lambda[/tex]I)=det(A-([tex]\lambda[/tex]-r)I).
The eigenvalues would be [tex]\lambda[/tex] where the det(A-[tex]\lambda[/tex]I)=0
and det(A-([tex]\lambda[/tex]-r)I)=0.
So does that mean the eigen values for the first matrix are [tex]\lambda[/tex] =n and the second will be n+r?
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