# v is a set of ordered pairs (a, b) of real numbers. Sum and scalar multiplication are defined by: (a, b) + (c, d) = (a + c, b + d) k (a, b) = (kb, ka) (attention in this part)

v is a set of ordered pairs (a, b) of real numbers. Sum and scalar multiplication are defined by: (a, b) + (c, d) = (a + c, b + d) k (a, b) = (kb, ka) (attention in this part) show that V is not linear space.
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Margot Mill
If V is a linear space, we must have that lv=v,
for all v from V. Take for example v=(0,1)
Then lv=1(0,1)=(1*1,1*0)=(1,0)=/v.
Thus V is not linear space.