bases of the reals^2 (1 Viewer)

[SPrada]

question: find 3 different bases of R^2

My answer: I thought for R^2 there are only two standard base vectors e1,e2 where e1=(0,1) e2=(1,0) which spans every vector in R^2 and can be written as a unique linear combination. So what is the 3rd bases of R^2 or could the question be wrong?? Thanks

 

[InteGrand]

question: find 3 different bases of R^2

My answer: I thought for R^2 there are only two standard base vectors e1,e2 where e1=(0,1) e2=(1,0) which spans every vector in R^2 and can be written as a unique linear combination. So what is the 3rd bases of R^2 or could the question be wrong?? Thanks

There are only two standard basis vectors, but there are many different bases. Remember, a basis is not a vector itself, but rather a set of vectors such that everything in the space can be written as a unique linear combination of them.

For example, the set {(1, 1), (1, 0)} is another basis for R².

 

[SPrada]

Thanks InteGrand for good ans...