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 Post subject: Eigeneed some help!!! How do you solve for A? in P^-1AP=DPosted: Sat, 19 Mar 2011 22:31:00 UTC

Joined: Sat, 19 Mar 2011 22:18:46 UTC
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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..

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 Post subject: Re: Eigeneed some help!!! How do you solve for A? in P^-1AP=Posted: Sat, 19 Mar 2011 22:36:49 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
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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 your matrix looks like

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 Post subject: Re: Eigeneed some help!!! How do you solve for A? in P^-1AP=Posted: Sat, 19 Mar 2011 23:08:48 UTC
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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.

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 Post subject: Re: Eigeneed some help!!! How do you solve for A? in P^-1AP=Posted: Sat, 19 Mar 2011 23:14:52 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
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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.

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 Post subject: Re: please please forgive me obvious stupidityPosted: Sat, 19 Mar 2011 23:18:50 UTC
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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. !

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

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