Practice question · Select all that apply
Select every set of vectors that forms a BASIS for the plane R^2.
Hints
- A basis for R^2 needs exactly two independent vectors.
- Reject any pair where one vector is a multiple of the other, and reject single vectors.
Show the answer
- A. (1, 0) and (0, 1)
- B. (0, 1) and (2, 0)
- E. (1, 1) and (2, 1)
Why
A basis for R^2 is exactly two independent vectors. (1,0)&(0,1), (1,1)&(2,1), and (0,1)&(2,0) each qualify. (1,2)&(2,4) are dependent, and a single vector cannot span the plane.
Practise Linear Independence and Basis
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More questions on Linear Independence and Basis
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