Eigeneed some help!!! How do you solve for A? in P^-1AP=D

ihatemath · **Joined:** Sat, 19 Mar 2011 22:18:46 UTC **Posts:** 5

Find a 2x2 matrix such that vector [-5,5] and vector [-1,-2] are eigen vectors and 9 and -7 are eigenvalues respectively. im studying for a quiz and cant figure out where to go with this question. any hints or advice is appreciated.

Im guessing to use P^-1AP=D and i see where the P and P inverese come from and the eigenvalues are the diagonal of matrix D... but then what..

Shadow · **Posted:** Sat, 19 Mar 2011 22:36:49 UTC

ihatemath wrote:

Find a 2x2 matrix such that vector [-5,5] and vector [-1,-2] are eigen vectors and 9 and -7 are eigenvalues respectively. im studying for a quiz and cant figure out where to go with this question. any hints or advice is appreciated.

Im guessing to use P^-1AP=D and i see where the P and P inverese come from and the eigenvalues are the diagonal of matrix D... but then what..

Just use the definitions, it's easy, remember that in the basis $\left\{ \begin{pmatrix}-5 \\ 5\end{pmatrix},\begin{pmatrix} -1\\-2\end{pmatrix}\right\}$ your matrix looks like $\begin{pmatrix} 9 & 0 \\ 0 & -7\end{pmatrix}$

Matt · **Joined:** Wed, 1 Oct 2003 04:45:43 UTC **Posts:** 9632

ihatemath wrote:

Im guessing to use P^-1AP=D and i see where the P and P inverese come from and the eigenvalues are the diagonal of matrix D... but then what..

The columns of P are the (linearly independent) eigenvectors.

Shadow · **Posted:** Sat, 19 Mar 2011 23:14:52 UTC

Matt wrote:

ihatemath wrote:

Im guessing to use P^-1AP=D and i see where the P and P inverese come from and the eigenvalues are the diagonal of matrix D... but then what..

The columns of P are the (linearly independent) eigenvectors.

And with both of our hints, the problem is completely trivial.

Happy hunting.

Shadow · **Posted:** Sat, 19 Mar 2011 23:18:50 UTC

ihatemath wrote:

i can find vector and values all day and I see how to arrange the formula and im positive ill feel quite sheepish when i figure it out, but im still having trouble... aahhhhh. ! :oops:

Just look at your formula, Matt has given you P and I have given you D.

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Eigeneed some help!!! How do you solve for A? in P^-1AP=D

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