Notice that for 6 (b) you don't need to use Gram-Schmidt, as
{F1,F2,F3} is already an orthogonal set. All you need to do here is to normalize each of the
Fi so that
<Fi,Fi>=1.
Then you use Gram-Schmidt in part (c) - but note here that the process only needs to be applied to
G as the others are already orthogonal.
N.B. I think there's a typo in the part (iii) of the question:
{F1,F2,F3,F4} can't be orthonormal - you've been asked to make
{F1,F2,F3} orthonormal in part (ii) of the question! So looks like the question should read "orthogonal" or should be asking for an orthonormal
{F1′,F2′,F3′,F4′}, where
{F1′,F2′,F3′} was the orthonormal basis constructed in part (ii).