I'm trying to solve this problem. But when I search I find different situations.
My question is
V is a subspace of R³. What are the possible dimensions to V?
Thank you guys.
2026-03-29 09:11:48.1774775508
V is a subspace of R³. What are the possible dimensions to V?
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$V$ can have dimension $0,1,2$ or $3$. Take for instance the origin, for the $0$-dimensional space. You could use the spaces spanned by any $1,2$ or $3$ linearly independent vectors, as examples. Well, in the case of dimension $1$, just the span of a nonzero vector...
As to the possibility of fractional dimension, i found this.
Maybe there are more possibilities...