Show that if x and y are not both 0 in z/nz then A(x;y) is not (0;0). Where (x;y) and (0;0) are 1x2 matrices.

Favorites|Homepage
Subscriptions | sitemap

HOME > Mathematics > Show that if x and y are not both 0 in z/nz then A(x;y) is not (0;0). Where (x;y) and (0;0) are 1x2 matrices.

Show that if x and y are not both 0 in z/nz then A(x;y) is not (0;0). Where (x;y) and (0;0) are 1x2 matrices.

[From: ] [author: ] [Date: 11-05-10] [Hit: ]

A(x) = 0 if and only if x = 0, from which your result follows.......

We are told A is the 2x2 matrix (a,b;c,d) in z/nz where D=ad-bc and gcd(D,N)=1. Im thinking it could be something to do with invertibility of the matrix but im not too sure, Thanks for any help

-

The usual 2x2 matrix inverse formula works in general over commutative unital rings and not just fields. That is, if the matrix's determinant has a multiplicative inverse, the usual formula (see my reference) works. Since gcd(D, n) = 1, D indeed has a multiplicative inverse, so A has an inverse. In particular, A(x) = 0 if and only if x = 0, from which your result follows.

1

keywords: Show,nz,that,are,not,and,is,matrices,in,Where,if,both,then,Show that if x and y are not both 0 in z/nz then A(x;y) is not (0;0). Where (x;y) and (0;0) are 1x2 matrices.

New

Hot