Let $R$ be a Noetherian ring and $I$ be a $R$-ideal. Then the symmetric algebra $sym(I)$ is the Tensor algebra modulo the ideal generated by forms $a\otimes b-b\otimes a$ where $a,b\in I$.
But I found papers where they present $sym(I)$ as $R[T_1, \cdots,T_m]/J$ where $J$ is the ideal generated by $\sum a_{ij} T_j$ where $(a_{ij})$ is the presentation matrix of $I$.
Is this easy to prove or is there a nice reference to this?