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Let W be a subspace of a (not necessarily finite-dimensional) vector space V. Prove that

Chapter 1, Problem 4

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QUESTION:

Let W be a subspace of a (not necessarily finite-dimensional) vector space V. Prove that any basis for W is a subset of a basis for V.

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QUESTION:

Let W be a subspace of a (not necessarily finite-dimensional) vector space V. Prove that any basis for W is a subset of a basis for V.

ANSWER:

Step 1 of 3

If is andimensional vector space and if  is a linearly independent set then we can extend  to  as a basis for V.

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