# Finite dimensional linear submanifold of N is complete.

Suppose that N is a normed linear space. Prove that each finite dimensional linear submanifold of N is complete and therefore closed.

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#### Solution Preview

Please see the attached file.

Suppose that is a normed linear space.

Let be a finite dimensional linear submanifold of .

Hence itself is a finite dimensional normed linear space.

Now we have to prove that is complete and therefore closed.

Let B = be a basis for so that

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#### Solution Summary

This solution is comprised of a detailed explanation of the problem on a normed linear space.

It contains step-by-step explanation for the following problem:

Normed Linear Space:

Suppose that N is a normed linear space. Prove that each finite dimensional linear submanifold

of N is complete and therefore closed.

Solution contains detailed step-by-step explanation.