Given the set $A=\{-100,-50,-1,1,2,4,8,16,32,2003\} . A$'s all non-empty subsets are denoted as $A_{1}, i=1,2, \cdots, 1023$. The product of all elements in each $A$, is denoted as $a, i=1,2, \cdots$, 1023. Then $a_{1}+a_{2}+\cdots+a_{1023}$ is
(A) 0
(B) 1
(C) -1
(D) 1023
1. (C).

Let the elements of $A$ be $x_{1}, x_{2}, \cdots, x_{10}$, then $a_{1}+a_{2}+\cdots+a_{1023}=\left(1+x_{1}\right)\left(1+x_{2}\right) \cdots\left(1-x_{10}\right)$ -1. Note that one of $x_{1}, x_{2}, \cdots, x_{10}$ is -1, hence $a_{1}+a_{2}+\cdots+a_{1023}=-1$.