Solve Eigenvalue Problem A: Proving (λI-A)=0 with Simetric Matrices

[nhrock3]

A is a simetric metrices nxn. so $$v\in R^n$$ and $$v\neq 0$$

so $$(\lambda I -A)^2=0$$ for some $$\lambda$$



prove that for the same $$v$$ $$(\lambda I -A)=0$$



how i tried to solve it:

i just collected data from the given.

simetric matrices is diagonizable.

$$B=(\lambda I -A)$$

we were given that $$B^2v=0$$

so $$B^2v \bullet v=0$$ (dot product is also v)

so v is orthogonal to $$B^2v$$



what to do now?

 

[ardie]

have u tried reading your own post?

 

[nhrock3]

have u tried reading your own post?

in latex not working here don't know why

yes i have tried to read this

even without the $$its very simple latex$$

 

[ardie]

ok i can read it now, so you are given that

A is a simetric metrices nxn. so $$v\in R^n$$ and $$v\neq 0$$

what is v?
so you are given this:

so $$(\lambda I -A)^2=0$$ for some $$\lambda$$

and you need to prove this?

prove that for the same $$v$$ $$(\lambda I -A)=0$$