# How to write an expression to represent z in terms of x_i and y_i?

For two vectors $z\in {R}^{d}$ and a scalar ${y}_{i}\in R$, and a symmetric matrix $A,B,C\in {R}^{d×d}$, if we have
$\sum _{i=1}^{n}\left[{y}_{i}AB-zC\right]=0$
But how to write an expression to represent z in terms of ${x}_{i}$ and ${y}_{i}$? Something likez=?....
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gerasseltd9
Let $z=\left({z}^{1},\dots ,{z}^{d}\right)$, ${x}_{i}=\left({x}_{i}^{1},\dots ,{x}_{i}^{d}\right)$ and $s=\sum {y}_{i}$. Then
$\frac{\sum {x}_{i}{y}_{i}}{\sum {y}_{i}}=\frac{{y}_{1}}{s}{x}_{1}+\cdots +\frac{{y}_{n}}{s}{x}_{n}=\left(\frac{{y}_{1}}{s}{x}_{1}^{1},\dots ,\frac{{y}_{1}}{s}{x}_{1}^{d}\right)+\cdots +\left(\frac{{y}_{n}}{s}{x}_{n}^{1},\dots ,\frac{{y}_{n}}{s}{x}_{n}^{d}\right),$
so
${z}^{j}=\frac{{y}_{1}}{s}{x}_{1}^{j}+\cdots +\frac{{y}_{n}}{s}{x}_{n}^{j}=\sum _{i}\frac{{y}_{i}}{s}{x}_{i}^{j}=\frac{1}{s}\sum _{i}{y}_{i}{x}_{i}^{j}$
where $1\le j\le d$