M is a 2 x 2 matrix with each of the 4 elements being real. Can there exist an integer G ≥ 2, for which the following relationship is satisfied?
[0 1]
M^{G} = 
[0 0]
If the answer to the above question is "no", prove it. Otherwise, cite an appropriate example.
(In reply to
Solution by Brian Smith)
Playing with your idea.
M^n = [a^n na^(n1)b]
[0 a^n ]
If b=1/(2a^(n1)) this becomes
M^n = [a^n 1 ]
[0 a^n]
If a<1 this matrix tends to the [M]^G sought in the limit as n → ∞
(I know this isn't a solution. I just thought it was interesting.]
Edited on June 22, 2009, 1:44 pm

Posted by Jer
on 20090622 13:37:20 