I have 3 vectors, A, B, C. They all have the same number of rows. What I am looking for is the all possible combination of summation of vectors. For this example, I want to have A+B, A+C, B+C, and A+B+C. Is there any command/package that can do that? In another words, I want all possible linear combinations of the 3 vectors with linear coefficients of 1. My real problem involves a lot of vectors, not just 3. I simplified it here.

Thanks