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If I have this matrix:

\begin{array}{cc}0&1\\1&0\end{array}

and I want to find its eigenvectors and eigenvalues, I can try it using the definition of an eigenvector which is:

Ax= λx ,where x are the eigenvectors

But if I try this directly I fail to get the right answer, for example using a column eigenvector (a b) , instead I get:

(b a) = λ (a b) , (These are column vectors.)

THere is no lambda able to make this correct, unless it is zero which is not the right answer. Why is that this approach didn't work?

I have to use the identity matrix, and the determinant of A - λ I, to get the right result.

Thanks!

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# B Elementary eigenvector question

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