Question

# 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)

Vectors

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.

If V is a linear space, we must have that $$lv=v$$,
for all v from V. Take for example $$v=(0,1)$$
Then $$lv=1(0,1)=(1 \cdot 1,1 \cdot 0)=(1,0)= v.$$