I have a vector $$ \mathbf{x} = (x_{21},x_{31},x_{32},x_{41}, x_{42}x_{51} , x_{52} , x_{53} , x_{54})^T $$ and I need to find a way, using some matrix operations, to derive this matrix here $$ \left( \begin{array}{ccccc} 1& 0 & 0 & 0 & 0 \\ x_{21} & 1 & 0 & 0 & 0\\ x_{31} & x_{32} & 1 & 0 & 0\\ x_{41} & x_{42} & -(x_{31}x_{41}+x_{32}x_{42}) & 1 & 0\\ x_{51} & x_{52} & x_{53} & x_{54} & 1\\ \end{array} \right) $$ Is that possible?
If that is not possible, it may be sufficient to obtain just a vector with the non-zero elements of a selected column.
Thanks