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12.1 Example: System of Nonlinear Algebraic Equations

For systems of linear algebraic equations, we recommend solving the system using matrix division. The algebraic solver becomes handy when we want to solve nonlinear equations.

As an illustrative example, we consider the following nonlinear system of two equations with two unknowns:

$$z_1 = y_1 - \theta_1 \\ z_2 = y_1 y_2 + \theta_2$$

Our goal is to simultaneously solve all equations for $y_1$ and $y_2$, such that the vector $z$ goes to 0.