Equations

Any two or more mathematical expressions (often polynomials) separated by the $=$ symbol. Systems of equations can also be represented as matrices:

[Differential Equations](Differential Equations.md)

As equations at it’s most basic level is a rather direct application of the law of identity (from Logic), it can be used to propose any identical relationship. Here is a example using vectors:

$x\begin{bmatrix}1 \\ 0 \\ 2\end{bmatrix} + y\begin{bmatrix}-1 \\ -2 \\ 1\end{bmatrix} = \begin{bmatrix}4 \\ 2 \\ -1\end{bmatrix}$

As equations are essentially logical propositions, they evaluate as either true or false. Therefore, if you have a “invalid” equation, it is really just a false logical proposition (removes some complexity). Try and see whether the examples here are true or false propositions.