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