How do I know the span of a matrix I have a marix that is 
$$R=\pmatrix{1&1&1\\1&1&1+2a\\0&2&2+2b}$$
and the span of R is   span=$\left\{\pmatrix{1\\1\\0},\pmatrix{0\\0\\1}\right\}$
In my preliminery thinking, the span is the combination of vectors that indicate each vector in R, but in reverse, If I know a matrix, how can I derive the span?
Could anyone tell me I can I calculate the span of a matrix
Taking this as an example, how can I get to this result?

You do not speak about span of matrices (in a vector space where matrix considered an abstract vector). In your case you should speak about column space $col(R)=Span\{R_{\downarrow j}\}_{j=1}^n$ or row space $row(R)=Span\{R_{i\rightarrow}\}_{i=1}^m$ of a matrix. There is also another related space, a null space, i.e. $Null(A)=\{x|Ax=0\}$. 
The Span's argument, i.e. the set in the curly brackets may be reduced in case of the vectors, columns or rows respectively, are not linearly independent. More precisely you can remove any linearly dependent vector without changing the space this set spans. 
Now to find the linearly independent vectors you simply produce with matrix
reduction. For the rows you throw away the zero rows. For the columns only the pivot columns are linearly independent.
