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I asked a question about symbolic matrices and LU decompositions in https://ask.sagemath.org/question/62878/how-to-define-a-matrix-with-variables-in-sagemath/

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 $T$ 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.

I asked a question about symbolic matrices and LU decompositions in https://ask.sagemath.org/question/62878/how-to-define-a-matrix-with-variables-in-sagemath/

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. much.

I asked a question about symbolic matrices and LU decompositions in https://ask.sagemath.org/question/62878/how-to-define-a-matrix-with-variables-in-sagemath/

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.