[SOLVED] Invertible and diagonal matrix

**mybrohshi5** · April 3rd 2010, 03:00 PM

Let A = $\begin{bmatrix}3&-\frac{1}{2}\\-6&5 \end{bmatrix}$

Find an invertible $S$ and a diagonal $D$ such that $S^{-1}AS = D$

S = $\begin{bmatrix}.&. \\.&. \end{bmatrix}$

D = $\begin{bmatrix}.&.\\.&. \end{bmatrix}$

I have never seen a problem like this and i am just a little confused on where to begin..

Thank you for any help

**NonCommAlg** · April 3rd 2010, 07:39 PM

Originally Posted by mybrohshi5

Let A = $\begin{bmatrix}3&-\frac{1}{2}\\-6&5 \end{bmatrix}$

Find an invertible $S$ and a diagonal $D$ such that $S^{-1}AS = D$

S = $\begin{bmatrix}.&. \\.&. \end{bmatrix}$

D = $\begin{bmatrix}.&.\\.&. \end{bmatrix}$

I have never seen a problem like this and i am just a little confused on where to begin..

Thank you for any help

on the main diagonal of D put the eigenvalues of A and the columns of S are the eigenvectors corresponding to the eigenvalues of A.

**mybrohshi5** · April 3rd 2010, 08:28 PM

This is what i got but it says it is wrong.

for my eigenvalues i got

$\lambda_1 = 2$ and $\lambda_2 = 6$

from my eigenvalue of $\lambda_1 = 2$ i got the eigenvector of
$\begin{bmatrix}\frac{1}{2}\\1\end{bmatrix}$

from my eigenvalue of $\lambda_2 = 6$ i got the eigenvector of
$\begin{bmatrix}\frac{1}{6}\\1\end{bmatrix}$

so for my S matrix i got

S = $\begin{bmatrix}\frac{1}{2}&\frac{1}{6} \\ 1&1\end{bmatrix}$

D = $\begin{bmatrix}2&0\\0&6\end{bmatrix}$

Can you see what i did wrong?

Thanks for the help

**mybrohshi5** · April 3rd 2010, 08:35 PM

Never mind i got it. the 1/6 is supposed to be a -1/6

Thanks again for the help

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