# `daetools`::`incidenceMatrix`

Find incidence matrix of system of equations

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## Syntax

````A` := daetools::incidenceMatrix(`eqs`,`vars`)
```

## Description

`A := daetools::incidenceMatrix(eqs,vars)` for `m` equations `eqs` and `n` variables `vars` returns an `m`-by-`n` matrix `A`, where `A[i,j] = 1` if `eqs[i]` contains `vars[j]` or any derivative of `vars[j]`. All other elements of `A` are `0`s.

## Examples

### Example 1

Find the incidence matrix of a system of five equations in five variables.

Create the following vector `eqs` containing five symbolic differential equations.

```eqs := [diff(y1(t),t) = y2(t), diff(y2(t),t) = c1*y1(t) + c3*y3(t), diff(y3(t),t) = y2(t) + y4(t), diff(y4(t),t) = y3(t) + y5(t), diff(y5(t),t) = y4(t)]:```

Create the vector of variables. Here, `c1` and `c3` are symbolic parameters (not variables) of the system.

`vars := [y1(t), y2(t), y3(t), y4(t), y5(t)]:`

Find the incidence matrix `A` for the equations `eqs` with respect to the variables `vars`.

`A := daetools::incidenceMatrix(eqs, vars)`

## Parameters

 `eqs` A list or a vector of equations or expressions in the state variables `vars` and their derivatives. Expressions represent equations with `0` right side. `vars` A list or a vector of identifiers or expressions, such as ```[x1(t), x2(t)]```.

## Return Values

A matrix of `1`s and `0`s.

#### Mathematical Modeling with Symbolic Math Toolbox

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