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I think should be all the combinations.

you get rid off was many vectors as needed to make them independent (but no more)

*of

yes

That's weird. So you can have three different basis for the set of vectors?

Does this mean that basis is not unique?

correct the basis is not unique...there can be an infinite number of basis's

Is there a condition where a basis will be unique?

|dw:1336751060283:dw||dw:1336751083709:dw|
both a basis for \(\mathbb{R}^2\)

you would have to be pretty restrictive

What a bais for a vector space? Can that be infinite as well?

yes

and you can do this by multiplying the basis by a scalar?

to get infinite basis?