For two vectors $z\in {R}^{d}$ and a scalar ${y}_{i}\in R$, and a symmetric matrix $A,B,C\in {R}^{d\times d}$, if we have

$$\sum _{i=1}^{n}[{y}_{i}AB-zC]=0$$

But how to write an expression to represent z in terms of ${x}_{i}$ and ${y}_{i}$? Something likez=?....

$$\sum _{i=1}^{n}[{y}_{i}AB-zC]=0$$

But how to write an expression to represent z in terms of ${x}_{i}$ and ${y}_{i}$? Something likez=?....