Rank of non-square matrix

Question

Let's be to the point: How to find rank of a non square matrix like $$ \begin{pmatrix} 1 & 1 & 1 \\ 3 & 2 & 1 \\ 1 & 1 & 0 \\ 1 & 0 & 0 \end{pmatrix} $$

I know that for square matrix we follow Gaussian Elimination Method converting the matrix into Echelon form and it's easy figuring out the rank of the matrix from there. But what about non square ones?

Answer 1

Hint: Rank is the dimension of the vector space generated (or spanned) by its columns. Therefore, since row operations do not change the rank, whether your matrix is square or not, the rank is always the number of pivots or leading coefficients in the echelon form.