hi.

i need to find the eigenvalues and eigenvectors of the following matrix.

( 7 -6 )

( -6 -2 )

i worked out the eigenvalues to be -2 and 7. can anyone tell me if these are right. not sure how to get eigenvectors.

thanks for the help

Printable View

- Mar 6th 2007, 02:35 PMmesterpaeigenvalues and vectors
hi.

i need to find the eigenvalues and eigenvectors of the following matrix.

( 7 -6 )

( -6 -2 )

i worked out the eigenvalues to be -2 and 7. can anyone tell me if these are right. not sure how to get eigenvectors.

thanks for the help - Mar 6th 2007, 02:53 PMJhevon
sorry, but those are wrong:

recall that to find the eigenvalues, we find det((lambda)In - A)

where In is the identity matrix and A is the matrix you're working on. i will use L for lambda, since i cant bother typing lambda all the time.

For eigenvalues:

det(L*In - A) = 0

(L..........0)......-.......(7...........-6)

(0..........L)..............(-6..........-2)

= (L - 7.........6)

...(6.......... L+2)

det(L - 7.........6) = 0

....(6.......... L+2)

=> (L - 7)(L + 2) - 36 = 0

=> L^2 -5L - 50 = 0

=> (L + 5)(L - 10)=0

so L1 = -5, L2 = 10 .............these are the eigen values - Mar 6th 2007, 02:55 PMThePerfectHacker
- Mar 6th 2007, 02:57 PMJhevon
to get the eigenvectors, you use (L*In - A)x = 0 where x is a vector of with components x1, x2 ....

so for each eigenvector, you plug in its value into the matrix that we formed, solve for the unknowns and place them in a solutions vector, these vectors will be your eigen vectors