Difference between vector basis and bases?

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The discussion clarifies that "bases" is simply the plural of "basis" in the context of vector spaces. It explains that a vector space can have multiple bases, using R2 as an example. The standard basis for R2 is {(1, 0), (0, 1)}, but other sets like {(1, 1), (1, -1)} also qualify as bases. Any two non-scalar multiple vectors in R2 can form a basis. Understanding these concepts is crucial for grasping linear algebra fundamentals.
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Could someone please explain the difference? Maybe show some examples?
Than you!

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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.
 

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