How to rewrite this matrix form

Question

I had this equation. \begin{equation} \begin{pmatrix} g_{1,1} & g_{1,2} & \cdots & g_{1,n} \\ g_{2,1} & g_{2,2} & \cdots & g_{2,n} \\ \vdots & \vdots & \ddots & \vdots \\ g_{n,1} & g_{n,2} & \cdots & g_{n,n} \end{pmatrix} \begin{pmatrix} p_1\\ \vdots\\ \vdots\\ p_n \end{pmatrix}= \begin{pmatrix} x_1\\ \vdots\\ \vdots\\ x_n \end{pmatrix} \end{equation} Is there any way that I can find \begin{pmatrix} \frac{1}{x_1}\\ \vdots\\ \vdots\\ \frac{1}{x_n} \end{pmatrix} in terms of G matrix and p vector?