Let V = â„‚2 be the vector space over the field of complex numbers and Bï€½{(1, i), (i,1)}be a given ordered basis of V. Then for which of the following, B* = {f1, f2}is a dual basis of B over â„‚? Options: A . &nbspf1(z1, z2) = 1/2 (z1 - iz2), f2(z1, z2) = 1/2 (z1 + iz2) B . &nbspf1(z1, z2) = 1/2 (z1 + iz2), f2(z1, z2) = 1/2 (iz1 + z2) C . &nbspf1(z1, z2) = 1/2 (z1 - iz2), f2(z1, z2) = 1/2 (-iz1 + z2) D . &nbspf1(z1, z2) = 1/2 (z1 + iz2), f2(z1, z2) = 1/2 (-iz1 - z2)

Let V = â„‚2 be the vector space over the field of complex numbers and Bï

Question

Let V = â„‚2 be the vector space over the field of complex numbers and Bï€½{(1, i), (i,1)}be a given ordered basis of V. Then for which of the following, B* = {f1, f2}is a dual basis of B over â„‚?

Options:

A . f1(z1, z2) = 1/2 (z1 - iz2), f2(z1, z2) = 1/2 (z1 + iz2)

B . f1(z1, z2) = 1/2 (z1 + iz2), f2(z1, z2) = 1/2 (iz1 + z2)

C . f1(z1, z2) = 1/2 (z1 - iz2), f2(z1, z2) = 1/2 (-iz1 + z2)

D . f1(z1, z2) = 1/2 (z1 + iz2), f2(z1, z2) = 1/2 (-iz1 - z2)

Answer: Option C

-NA-

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