Practice question · Multiple choice
and together span only the line , while and span the whole plane. What does that show about counting vectors?
Hints
- Ask whether can be written using .
- Dimension counts directions, not vectors.
Show the answer
C. That the number of vectors does not determine the dimension
Why
A dependent vector adds no new direction. This is exactly why rank is defined as the number of independent columns rather than the number of columns.
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