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Powers of a 2x2 matrix

  1. Apr 14, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the nth power of the matrix A,

    |1 1|
    |0 0|

    2. Relevant equations

    3. The attempt at a solution

    My guess is the A^n = PD^nP^-1 formula. But my prof says not use to eigenvalues and eigenvectors. Is it possible to solve this without using the formula A^n = PD^nP^-1 ???
  2. jcsd
  3. Apr 14, 2009 #2
    Is it specifically [tex] {1\, 1 \choose 0\, 0} [/tex] or a more general problem?

    Have you tried calculating any powers of that particular matrix?

    [tex] {1\, 1 \choose 0\, 0}{1\, 1 \choose 0\, 0} = {1\, 1 \choose 0\, 0} [/tex]

  4. Apr 14, 2009 #3
    Let's say more general.

    Is it just calculating successive powers and finding some pattern to base a formula off of?
  5. Apr 14, 2009 #4
    It depends what level a course the problem is being asked in, really. For something like this, the pattern is incredibly obvious. In general, there may not be a pattern though... But, if your teacher/professor is looking for a simple solution without much technical mathematics, which it sounds like, doing some sample calculations and finding a pattern is a solid plan (especially for this particular matrix).
  6. Apr 14, 2009 #5
    This is Calculus 4. Pattern finding is probably the most obvious solution. Thanks for the help.
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