I'm a bit confused about finding the dimensions of vectors spaces.
For example, the space $V=\{\mathbf0\}$ has dimension $1$ or $0$?
How do I find the dimension of a vector space?
If $V=span\{\mathbf e_1, \mathbf 0\}$, then $dimV=1$ or $2$?
Vector space dimensions
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linear-algebra
vector-spaces
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0$V=\{e_1,0 \}$ doesn't make sense. Maybe you meant $V=\text{span}\{e_1,0 \}$, which you would write $V=\text{span}\{e_1\}$ – 2017-02-15
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1By definition, the dimension of a vector space is the number of vectors in a basis of that vector space. (The vectors in a basis must be nonzero vectors.) Accordingly zero vector space has dimension zero. As for $V = \{{\bf e}_{1}, {\bf 0}\}$, it is not a vector space at all. It is just a set of vectors. – 2017-02-15
1 Answers
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Hint: (Definition) Dimension of a vector space is the number of linearly independent basis vectors it has.
Note: $\textbf0$ vector can be generated by $\textbf e_1$ by using the scale factor $0$ and thus $\textbf0$ vector doesn't contribute to the basis in the above definition in the hint.