Example of Linear functional on subspace which cannot have extension

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I wanted to find example of linear functional on subspace of vector space which cannot be extended to whole vector space.

I know that if we are in normed linear space then extension is always possible also even if we are in vector space with some additional condition on bound using Minkowski functional [By Hanh Banach theorem Analytic form ] we have extension .

I tried to find that but I did not get Any Help will be appreciated Thanking you