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Proof by induction

  • Thread starter annoymage
  • Start date
  • #1
362
0

Homework Statement



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

Homework Equations



n/a

The Attempt at a Solution



how do you proof by induction when there's 2 variable?
 

Answers and Replies

  • #2
362
0
1-n , -n



n , 1+n
 
  • #3
1,953
248
Show that AnAm = An+m

Homework Equations



n/a

The Attempt at a Solution



how do you proof by induction when there's 2 variable?
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]
 
  • #4
362
0
oooo, i see i see,
thank you very much. :)
 
  • #5
1,953
248
It's actually easier to just compute the product of A_m and A_n
 
  • #6
362
0
yeaaa, it is, why didn't i think of that. =.=

hoho thanks again
 

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