It says: Show that v is an eigenvector of A and find the corresponding eigenvalue.

A =

[3 0 0

0 1 -2

1 0 1]

v =

[2

-1

1]

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- March 22nd 2010, 07:10 AMnicolem1051Eigenvectors and Eigenvalues
It says: Show that v is an eigenvector of A and find the corresponding eigenvalue.

A =

[3 0 0

0 1 -2

1 0 1]

v =

[2

-1

1] - March 22nd 2010, 08:55 AMTheEmptySet
- March 22nd 2010, 09:54 AMnicolem1051
thank you so much, that's the answer I got but I don't understand why it is 3. For some reason I am not getting it(Doh)

- March 22nd 2010, 11:46 AMcanto88
to find the eigenvalues all u have to do is find the characteristic equation det(A-λI)=0

for example..the matrix A[ 3 0 0

0 1 -2

1 0 1]

u write it like this A[ 3-λ 0 0

0 1-λ -2

1 0 1-λ]

and then you expand by Column 2

and therefore u get (1-λ)(3-λ)(1-λ)=0

hence the eigenvalues are λ=1, λ=3, λ=1.

You can now find the corresponding eigenvectors u, v and w.

Let u=[a,b,c]. If Au=λu where λ=1 and 3 in this case. u solve the system Au=λu and u find the eigenvectors.