I am looking for a free resolution of the ideal generated by $2\times 2$-minors of a $3\times 3$ -matrix. More precisely let $M$ be a matrix (sorry but I cannot write a matrix for some TeX technical reason) $$ M=\begin{bmatrix} x_{1},& x_{2},& x_{3}:\ \ x_{4},& x_{5},& x_{6}: \ \ x_{7},& x_{8},& x_{9} \end{bmatrix} $$ whose entries are indeterminates. I would like to find a free resolution of the ideal generated by $2\times 2$-minors of $M$ in the ring $\mathbb{C}[x_{1},\dots,x_{9}]$.

Does anyone know the reference for this resolution? Or make one for me.

I am looking for a free resolution of the ideal generated by $2\times 2$-minors of a $3\times 3$ -matrix. More precisely let $M$ be a matrix (sorry but I cannot write a matrix for some TeX technical reason) $$ M=\begin{bmatrix} x_{1}& x_{2}& x_{3} \\\ x_{4}& x_{5}& x_{6} \\\ x_{7}& x_{8}& x_{9} \end{bmatrix} $$ whose entries are indeterminates. I would like to find a free resolution of the ideal generated by $2\times 2$-minors of $M$ in the ring $\mathbb{C}[x_{1},\dots,x_{9}]$.

Does anyone know the reference for this resolution? Or make one for me.