# Thread: Show that if Ax=b has more than 1 solution, it has infinitly many solutions

1. ## Show that if Ax=b has more than 1 solution, it has infinitly many solutions

Show that if Ax=b has more than 1 solution, it has infinitly many solutions.

Hint: If $u_1$ and $u_2$ are two solutions consider $w=ru_1+su_2$ where $r+s=1$

Here's my start
let $u_1$ and $u_2$ be distinct solutions to $Ax=b$ then $Au_1=b$ and $Au_2=b$

Why must r+s=1?

2. Originally Posted by Jskid
Hint: If $u_1$ and $u_2$ are two solutions consider $w=ru_1+su_2$ where $r+s=1$

Here's my start
let $u_1$ and $u_2$ be distinct solutions to $Ax=b$ then [maht]Au_1=b[/tex] and $Au_2=b$

Why must r+s=1?
$A(r u_1 + su_2) = b (r + s)$ ....