Dimension of the span of vectors I am sorry for quite a silly question.
What is the dimension of the span of $2$ linearly dependent vectors over $\mathbb{R}^3$.
For example, I have $v=(1, 2, 1)$ and $u=(2, 4, 2)$.
 A: The span has dimension 2 if and only if your vectors are not  one multiple of the other.
In the case you prpposed  $(2,4,2)=2\cdot(1,2,1)$ and the span has dimension 1.
A: For a finite dimensional vector space, the dimension is the number of elements in a basis (any basis will have the same number of elements)
The span of vectors forms a subspace (and so is a vector space).
So, $v$ and $u$ span a subspace, but are not linearly independent so are not a basis for that subspace.
$v$ will also span your space, and $\{v\}$ is independent, so $\textbf{in your example}$ the answer should be 1.
A commenter was making the point that $\{0, 0\}$ is a linearly dependent set of two vectors in $\mathbb{R}^3$ that has dimension $0$, because the zero subspace is defined to have dimension $0$ (and is the only vector space of dimension $0$)
So, in summary, the subspace spanned by two linearly dependent vectors in $\mathbb{R}^3$ will have dimension $1$ unless they both happen to be the zero vector in which case the space has dimension $0$
