Re: Questions about nested intervals. Help me please!!!

Vadim Tropashko wrote:
> Remember, we (rather arbitrarily) selected node [[30,37],[73,90]] as a
> ... there is a matrix that satisfies the equation
>
> [[2,7],[5,17]]*[[a,b],[c,d]]=[[30,37],[73,90]]
>
> Here I take a little jump, assuming that finding a,b,c,d is easy for
> anybody with rudimentary linear algebra skills.

This is fairly easy. What is the inverse of [[2,7],[5,17]]? For 2x2 matrices the inverse calculation is trivial:

[[x11,x12],[x21,x22]]^(-1) =
det([[x11,x12],[x21,x22]]) * [[x22,-x12],[-x21,x11]]

which gives in this case

[[2,7],[5,17]]^(-1) = [[-17,7],[5,-2]]

Left mutiply

[[2,7],[5,17]]*[[a,b],[c,d]]=[[30,37],[73,90]]

both sides by [[-17,7],[5,-2]]

[[a,b],[c,d]]=[[-17,7],[5,-2]]*[[30,37],[73,90]]=[[1,1],[4,5]] Received on Tue Jul 19 2005 - 18:12:12 CDT