Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Proof by induction

  1. Feb 28, 2010 #1
    1. The problem statement, all variables and given/known data

    A= (1-n -n

    n 1+n)

    this is 2x2 matrix, sorry but i dont know which latex to use.


    Show that AnAm = An+m
    2. Relevant equations

    n/a

    3. The attempt at a solution

    how do you proof by induction when there's 2 variable?
     
  2. jcsd
  3. Feb 28, 2010 #2
    1-n , -n



    n , 1+n
     
  4. Feb 28, 2010 #3
    You do induction on one of the variables and leave the other with universal
    quantifier

    You take as base case: For all n [itex] A_n A_0 = A_{0+n} [/itex]

    and the induction hypthesis: For all n [itex] A_n A_m = A_{m+n} [/itex]

    and try to prove For all n [itex] A_n A_{m+1} = A_{m+1+n} [/itex]
     
  5. Feb 28, 2010 #4
    oooo, i see i see,
    thank you very much. :)
     
  6. Feb 28, 2010 #5
    It's actually easier to just compute the product of A_m and A_n
     
  7. Feb 28, 2010 #6
    yeaaa, it is, why didn't i think of that. =.=

    hoho thanks again
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook