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A = \[\left[\begin{matrix}1 & 1 & 1 \\ 1 & 1 & 1 \\ 0 & 0 & a\end{matrix}\right]\]

you must find all values in which the row <0,0,a> is linearly independent

im assuming Defective means it doesnt have a complete set of eigenvectors. is that wrong?

correct so find when row is linearly dependent

i understand 0 but not so much 2? how is that?

also We never went over this.. my book doesn't have this

book says a=2, btw.

did the book ask for non trivial?

i think you might be mistaking this with the Null Space, or kernel.

haha it didn't say anything about trivial.

Wait, how did you end up with λ(a−λ)(2−λ)=0?

i meant how did you get that as the determinant, to be more precise

scanning and posting in a sec.

okay thanks.

gotcha for some reason i must have got a sign error i got lambda - a

thats fine too. some people do det(lambda I - A)

ahh you were missing a negative lol

lolol

in my defense, the answer will be the same! lol