Give and prove an example of a subset A which is closed under scalar multiplication, but not under vector addition.
Give and prove an example of a subset A which is closed under vector addition but not under scalar multiplication.
1) See why its closed under scalar multiplication? but for instance is not in there.
2) Let A be the set of vectors with integer entries. So (1,1) is in there and it is clear that its closed under addition since the integers are.
But take .5(1,1) and it isnt in there anymore.