# LU decomposition for symbolic matrices with many different variables.

I asked a question about symbolic matrices and LU decompositions in https://ask.sagemath.org/question/628...

I have another question about LU decomposition. I would like to define a matrix $x_i(t)$ as a matrix with $1$'s on the diagonal and with $t$ at $(i,i+1)$ position, and all other entries are $0$. Let $g = x_{i_1}(t_1) \cdots x_{i_m}(t_m) T$, where $i_1, \ldots, i_m$ are some given integers, $T$ is a diagonal matrix with entries $\lambda_1, \ldots, \lambda_n$. I would like to define this matrix in Sage and apply LU decomposition to it. Now $t_1, \ldots, t_m, \lambda_1, \ldots, \lambda_n$ are symbols. How to do this in Sage? Thank you very much.