Question

Show that if n is a positive integer then, [{1,1}{0,1}] = [{1,n}{0,1}] (these are supposed to be 2x2 matrices)

Answer 1

oh, that was supposed to be [{1,1}{0,1}]^n = [{1,n}{0,1}]

Answer 2

does the equal sign refer to row equivalence?

Answer 3

oh, exponent stuff.

if show means prove, then you might have to use induction

Answer 4

establish a basis:

1 1 ^1 = 1 1
0 1 0 1 is true

let n=k to define it in a more generic manner


1 1 ^k = 1 k
0 1 0 1 is assume to be true


multiply both sides by 1 1
0 1 to get to the k+1 exponent


1 1 ^(k+1) = 1 k * 1 1
0 1 0 1 0 1



1 1 ^(k+1) = 1 k+1
0 1 0 0+1

Answer 5

so if it is true for some integer k, it is true for some integer k+1

we know it is true for k=n=1

Answer 6

thank you so much! I was thinking that I would have to use induction, but was not quite sure how to do it using matrices.

Answer 7

i just went with a gut feeling :)