# Create Matrix in RREF with indeterminates

Hi all,

I would like to be able to create a Matrix over a multivariable polynomial ring (in particular over R = PolynomialRing(QQ, 'x',(n-k)*n)) in Sage that has a particular form. I would like to create a $k \times n$ matrices that is in RREF form, where I can choose where the pivots should be and fill in the rest with variables from my polynomial ring. (I am assuming full rank, so there will be $k$ pivots with $n \choose k$ possible choices)

$\begin{bmatrix} 1 & x1 & 0 & x2 & \cdots\\ 0 & 0 & 1 & x3 & \cdots\\ 0 & 0 & 0 & 0 &\cdots \\ \vdots & \vdots & \vdots & \vdots & \ddots \end{bmatrix}$

Is there any way I can do this in Sage by just indicating which columns I want to have the pivots in?