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## Homework Statement

Let

[tex]

A = \left[ \begin{array}{cc} -6 & 0.25 \\ 7 & -3 \end{array} \right]

[/tex]

Find an invertible S and a diagonal D such that [tex]S^{-1}AS=D[/tex]

## Homework Equations

I basically have the question answered, just ONE problem.

## The Attempt at a Solution

My answer is:

[tex]

S = \left[ \begin{array}{cc} 1 & -1 \\ 14 & 2 \end{array} \right]

[/tex]

[tex]

D = \left[ \begin{array}{cc} -40 & 0 \\ 0 & -104 \end{array} \right]

[/tex]

I asked the professor what was wrong and he said "check the eigenvalues (main diagonal of D). The eigenvectors look ok, but their order has to match that of the eigenvalues.

I've checked over and over, the math works out(S^-1 A S = D) , but I can't see what's wrong with the order. It looks perfectly fine for me.

All I need to figure out is what the correct order is. Please help ><

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