Proof of eigenvalues?
How would one go about this proof: Any help would be great thank you!
Prove that if A is a 3x3 matrix with eigenvalues a,b,c, then A-kI will have eigenvalues a-k, b-k, c-k.
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The eigenvalues s of A-kI are solutions of |A-kI-sI|=0
=> |A-(k-s)I|=0
This means k-s are eigenvalues of A giving k-s=a or b or c
and you get the required values of s