Basis of a subspace can be extended to a basis of the vector space ↩

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created: 2021-11-14 02:30:54
modified: 2022-01-10 04:13:04

Proof

Let be a basis for (it is finite). Then is linearly independent in . If ¹, we are done.
If not, we take in so that:

We consider linearly independent subsets of and we can get a basis from it for containing .

Implications

• It implies that