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Let $V$ be a vector space defined by $V:=\text{span}\{(1,1,1), (1,−1,1),(1,2,3)\}$. How do I find the dimension of $V$?

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    What collection of those three vectors is linearly independent (i.e. are there 1,2, or 3 linearly independent vectors there)? – 2017-02-04
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    Do you know the definition of "dimension" for a space? – 2017-02-05

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Row reduce the matrix with column vectors equal to these vectors. The dimension is the number of non-zero rows.