Difference between vector basis and bases?

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misterau
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Homework Statement



Could someone please explain the difference? Maybe show some examples?
Than you!

Homework Equations





The Attempt at a Solution

 
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I am not sure I understand you correctly, "bases" is the plural of "basis".
 
A given vector space can have many bases. For example, R2 has the standard basis {(1, 0), (0, 1)}, but the following set is also a basis for R2--{(1, 1), (1, -1)}. In fact, any two vectors in R2 that aren't scalar multiples of each other would serve as a basis for R2.