3 Give an example of a subset W of the vector space R2 such

3. Give an example of a subset W of the vector space R^2 such that:

(a) W is closed under vector addition, 0 / W, and W is not closed under scalar multiplication.

(b) W is closed under scalar multiplication and W is not closed under vector addition.

Solution

a] Z(integers) over Q(rationals), which is closed under vector addition and not closed under scalar multiplication

b] The set of all non-square matriceswhose entries from real numbers, which may not be closed under vector addition and is closed under scalar multiplication.