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## Homework Statement

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 :/

Anyone? Thanks!