am i finding the eigenvalues the correct way?
from 3x3 matrix[9 4 0/-6 -1 0/6 4 3]. I end up with L^3 - 11L^2 +39L -45=0 ..how should i further simplify this to get the eigenvalues?

Question

am i finding the eigenvalues the correct way? 
from 3x3 matrix[9 4 0/-6 -1 0/6 4 3]. I end up with L^3 - 11L^2 +39L -45=0 ..how should i further simplify this to get the eigenvalues?

anonymous · Answer

well actually i got -L^3+13L^2-63L+99

anonymous · Answer

you are probably right..i just realized i made a mistake simplifying something

anonymous · Answer

wait i did some mistake too

anonymous · Answer

well i got -L^3+11L^2-39L-13

anonymous · Answer

i keep getting 45 instead of 13, but then how do i find the eigenvalues from there?

anonymous · Answer

lol yeah it is 45 sorry miss writing, actually if we can use calculator to find the L values, but without the calculator theres a technique to it which i forgot the name==

anonymous · Answer

do your college permit you to use calculator in exam?

anonymous · Answer

no

zzr0ck3r · Answer

expand around column three

(3-x)[(9-x)(-1-x)+24]
(3-x)(x^2-8x-15)
(3-x)(x-5)(x-3)

zzr0ck3r · Answer

so eigen values are 3,3,5

anonymous · Answer

ohhh i see! Thanks!

zzr0ck3r · Answer

det(A-xI) = 0
where x is eigen values

anonymous · Answer

can i ask too?, after finding the eigenvalues, how to find the eigenvector corresponding to it?
for example when the L=3

zzr0ck3r · Answer

when l = 3 subtract 3 from all the values on the diagonal and then set the matrix = to 0, then solve.

zzr0ck3r · Answer

ie find the null space of A - 3I where I is hte identity matrix

anonymous · Answer

okay thanks!

zzr0ck3r · Answer

np