Question

If A=
2 -2 -1
1 -1 -1
0 0 1
find all eigenvalues and eigenvectors of A.

thank you

Answer 1

Oh yay matrix.

Answer 2

Solve characteristic equation?

Answer 3

i have done all, but i get confused with the vectors

Answer 4

\[\det(A-\lambda I)=0\]

Answer 5

what eigenvalues did you get?

Answer 6

ill do em now

Answer 7

lambda = 0 and lambda =1

Answer 8

Can you row reduce to a triangle matrix before subtraction lambda I ?

Answer 9

i have to solve x-2y-z=0
that is the only equation i get

Answer 10

I got zero and one as well.

Answer 11

i solved it

Answer 12

Cool if you have more I would love to help

Answer 13

Yes I get \[\lambda=1,1,0\]as well

Answer 14

HAHA I'm so lame.
You don't have to do all the characteristic equation all the way. Just row reduce to triangle matrix and all the diaganol values of the matrix are the eigen values.

Answer 15

for \[\lambda =1\]i get \[2x-2y-z=0,\]