- #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 A

_{n}A

_{m}= A

_{n+m}

## Homework Equations

n/a

## The Attempt at a Solution

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

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- Thread starter annoymage
- Start date

- #1

- 362

- 0

A= (1-n -n

n 1+n)

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

Show that A

n/a

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

- #2

- 362

- 0

1-n , -n

n , 1+n

n , 1+n

- #3

- 2,010

- 288

Show that A_{n}A_{m}= A_{n+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. :)

thank you very much. :)

- #5

- 2,010

- 288

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

hoho thanks again

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