Question

Hi, I was wondering how do I row reduce this 2x2 matrix:
|1-x 1|
|1 -x| (where x represents a known eigenvalue)
down to
|1 -x|
|0 0|

Thank you.

Answer 1

I don't see how you could. Check the determinants; unless your eigenvalue is the Golden ratio

Answer 2

@inkyvoyd yes, how did you know?! This was part of a proof to find a general formula for the nth fibonacci number. (I think that's the golden ratio).

Answer 3

I didn't; I tried to match up your determinants and got the quadratic equation for the Golden ratio. That turns out to be the limit as n approaches infinity for the nth/(nth-1) fibonacci numbers, and it has to do with eigenvalues for sure, but unfortunately I don't ahve the required mathematical knowledge ot tell you why. There is a secction in my text though!

Answer 4

Hmm ok, I didn't quite get what you mean by the limit as n approaches infinity. Did you mean that the 2nd matrix is the limit of the first as n approaches infinity?

Answer 5

no no no, I was not talking about matrices but the fibonacci numbers themselves.

Answer 6

@Kainui @ganeshie these persons will probalby be more helpful :)

Answer 7

Ah right. Yep, I have no idea either. The first matrix was meant to be (M-(x)I)=0 where x is the golden ratio.