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.
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 :/