find the rank of the following matrix

$
\begin{bmatrix}
2 & 3 & -1 & -1 \
1 & -1 & -2 & -4 \
3 & 1 & 3 & -2 \
6 & 3 & 0 & -7
\end{bmatrix}
$

Please help !!!!

Question

find the rank of the following matrix

$
\begin{bmatrix} 
2 & 3 & -1 & -1 \
1 & -1 & -2 & -4 \
3 & 1 & 3 & -2 \
6 & 3 & 0 & -7
\end{bmatrix}
$

Please help !!!!

anonymous · Answer

should i try reducing it or any easy way out ?

anonymous · Answer

Use Gaussian Elimination to get into Reduced Row Echelon Form?

anonymous · Answer

I have just started linear algebra, is the gaussian elimination same as 3 elementary operations ?

phi · Answer

one way to find the rank of a matrix is put it in row echelon form see http://www.stattrek.com/matrix-algebra/echelon-transform.aspx and count the number of pivots, which will equal the matrix's rank

anonymous · Answer

row echleon form seems to be having more steps just for finding rank... 
textbook example shows to reduce it to triangular form, but i dont really get it completely.

anonymous · Answer

cuz triangular form for non-square matrix makes no sense, even if i try changing it to triangular form by making all elements below leading diagonal 0, i need to also check the determinants of top minors ?

phi · Answer

if you start with a full rank, square matrix, and reduce it to row echelon form, you will get an upper triangular matrix. but if it is not full rank, you will get some columns without a pivot. If you start with a rectangular matrix, row echelon form does not look particularly triangular to me.... see http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/lecture-2-elimination-with-matrices/