Practice question · Multiple choice
Why must every basis of have exactly three vectors, never two, never four?
Hints
- Ask what two vectors can reach in three dimensions.
- Then ask whether four vectors in can all be independent.
Show the answer
A. Because fewer cannot span and more must be dependent
Why
Two requirements squeeze from opposite sides and meet at the dimension. This is why dimension is well defined at all: every basis is forced to the same size.
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