If a vector space is infinite dimensional then prove that dual space is also infinite dimensional

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Consider this question: Let we have a vector space which is infinite dimensional then show that it's dual space is also infinite dimensional.

I have been reading notes on Manifolds from class notes of senior and this was left to do itself.

I have done a course on Linear algebra 2 years ago and followed Hoffman, Kunze but I can't recall now what result I should use and I looked back at it but not sure what result to use. So, can you please give some hints?