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)

cistG

cistG

Answered question

2021-06-20

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.

Answer & Explanation

saiyansruleA

saiyansruleA

Skilled2021-06-21Added 110 answers

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)=(11,10)=(1,0)=v.
Thus V is not linear space.

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