How to calculate the rank of a matrix?
The second column - first column is the last column so the rank is $<3$.
The first two colums are linearly independent so the rank is $2$.
Simply use row reduction: the rank is the number of non-zero rows after you've performed row reduction:
\begin{align}
&\begin{bmatrix}
3&2&-1\\2&-3&-5\\-1&-4&-3
\end{bmatrix}\rightsquigarrow
\begin{bmatrix}
1&4&3\\3&2&-1\\2&-3&-5
\end{bmatrix}\rightsquigarrow
\begin{bmatrix}
1&4&3\\0&-10&-10\\0&-11&-11
\end{bmatrix}\\[1ex]
\rightsquigarrow&\begin{bmatrix}
1&4&3\\0&1&1\\0&-11&-11
\end{bmatrix}\rightsquigarrow
\begin{bmatrix}
1&4&3\\0&1&1\\0&0&0
\end{bmatrix}
\end{align}
Thus, the rank is $2$.
Note that it was obvious after the second step.
The key word is row echelon form.