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Powering Up The Matrix (Posted on 2009-06-20) Difficulty: 3 of 5
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]
MG =|        |
        [0    0]

If the answer to the above question is "no", prove it. Otherwise, cite an appropriate example.

No Solution Yet Submitted by K Sengupta    
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re: Solution Comment 3 of 3 |
(In reply to Solution by Brian Smith)

Playing with your idea.  
M^n = [a^n  na^(n-1)b]
      [0    a^n      ]

If b=1/(2a^(n-1)) 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 2009-06-22 13:37:20

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