As I read one linear algebra book I have, I am told that "If a vector space V has a basis with 'n' vectors, then every basis in vector space V has 'n' vectors.(adsbygoogle = window.adsbygoogle || []).push({});

So every basis in R3 has 3, every basis in R4 has 4, etc.

However, I have a problem that says:

Let S = { "five vectors" } be a set of vectors in R4.

Find a subset of S that is a basis for W = span S.

The solution goes through putting the matrix into row-echelon form, and it turns out v1, and v2 of the set S are a basis for W = Span S.

I'm confused, I thought bases of R4 had four vectors? Could someone clear this up for me?

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# Homework Help: Linear Algebra - Number of vectors in a basis

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