anonymous
  • anonymous
is it possible for a vector space to have more than one basis?
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Yes.
phi
  • phi
sure, for example [1 0] and [0 1] [1 0] and [1 1] are both bases for 2-d space
anonymous
  • anonymous
ok then tell me if S={u1,u2,.....,un} and S'={v1,v2,....,vn} be two bases far a vectorspace V then v1=au1+bu2+......+zun ie every element of V(it can be v1 which is also the element of 2nd basis) can be written as a linear combination of basis vectors u1,u2,....un. how is it possible that a linearly independent vector i.e v1 in this case can b written as a linear combination of other linearly independent vectors. how???

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phi
  • phi
vectors are independent relative to all others in a set of vectors. In pictures: |dw:1328108084917:dw|
phi
  • phi
you can use the solid lines to identify every point (x,y) you could use the dotted lines (move so far down one of the dotted lines, and then so far in the direction of the other dotted line) to get to the same point. Each set is a basis.

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