Question : basic question about eigenvalues

Hi

I don't understand the explanation of eigenvalues given in my book. I have scanned in the relevant page and put comments on the page.

To me it looks as if you are multiplying out  matrices using the rules of matrices to get some 'normal equations' You then manipulate these equations as you would using normal rules for equations and then put the answer back into matrix form. This doesn't seem right. It then says 'note the unit matrix is introduced since we can only subtract a matrix from another matrix'

It all seems a bit of a hack somehow. Perhaps I'm reading it wrong

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Answer : basic question about eigenvalues

I'm not a math guy at all, however, I am a google guy.
Googled around a bit, and found:

http://mathworld.wolfram.com/Eigenvalue.html

Just from reading your book, and some google pages, I'd say "Yes" to using non matrix rules to subtract terms.  To me (not an expert, just a second opinion) it looks like you're going from matrices, to an equation, then back to a matrix.