1. The problem statement, all variables and given/known data a) construct a subset of two-dimensional space closed under vector addition and even subtraction, but not under scalar multiplication. b) construct a subset of two-dimensional space (other than two opposite quadrants) closed under scalar multiplication but not under vector addition. 3. The attempt at a solution a) A line going through a point on the y-axis. Not a line through the origin though. I figure since the line does not have a null-vector in it, it is not closed under scalar multiplication. b) I only know of two opposite quadrants :/ Anyone? Thanks!