If $$W$$ be a proper subspace of a finite dimensional vector space, then​

Correct option is C

Solution:

​• A subspace is a subset of a vector space that is itself a vector space under the same operations.
• A proper subspace means W⊂V and W≠V.
• In this case, the dimension of the subspace is strictly less than that of the full space.
So: $$\dim(W) < \dim(V) \Rightarrow \dim(W) \leq \dim(V)$$

Hence, the correct inequality that always holds is:
Final Answer: (C)
​$$\dim W \leq \dim {V}$$​​
​​

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