# Definition of stock-flow matrix and understanding it

I am asking a simpler question at here from Constructing and understanding stock-flow model (If one of them needs to be closed, keep this one.)

Suppose that $\textbf{x} = A\textbf{x} + B\dot{\textbf{x}}$ where $\textbf{x}$ is vector of economic output level, $A$ is input-output matrix (or consumption matrix), $B$ is stock-flow matrix. The system represents closed and dynamic input-output system. $\dot{\textbf{x}}$ is time derivative of $\textbf{x}$.

OK, so what exactly is $B$ doing? I do understand that $A\textbf{x} + \textbf{d} = \textbf{x}$, where $\textbf{d}$ refers to final demand vector (Link: http://www.cs.laurentian.ca/jdompierre/html/MATH2057E_F2008/cours/Leontief_IO.pdf), but then it would mean $\textbf{d} = B\dot{\textbf{x}}$ and I am unsure why $B$ is named stock-flow matrix, and how is $B$ multiplied with first time derivative of $\textbf{x}$ to produce $d$, final demand vector - or output that will be for consumers buying it in order to consume it - not for production. So, what exactly is $B$, or "stock-flow matrix"?

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