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## Homework Statement

a) Find a set of vectors in R2 that is closed under vector addition but not under scalar multiplication

Find a set of vectors closed under scalar multiplication but not closed under vector addition.

## The Attempt at a Solution

a) Let S be a set of vectors in R2.

S = {(x,y) | x + y =0}

x = (1,1) y = (-1,-1)

To show that S set of vectors is closed under vector addition, x + y must remain in S.

x + y = (x1 + y1, x2+y2) = ( 0,0)

Am I right up till here?