Question

only the Answers, Determine if the function defines an inner product on R², where u = (u₁, u₂) and v = (v₁, v₂). (Select all that apply.)

(u, v )= (u₁v₁ + u₂v₂)

a) satisfies (u,v)=(v,u)

b) does not satisfy (u, v)=(v,u)

c) satisfies (u, v+w) = (u,v)+(u,w)

d) does not satisfy (u, v+w) = (u,v)+(u,w)

e)satisfies c (u,v) = (cu, v)

f) does not satisfies c (u,v) = (cu, v)

g) satisfies (v, v) >= 0 and(v,v)=0 if and only if v=0

h) does not satisfies (v, v) >= 0 and(v,v)=0 if and only if v=0

Answer 1