# `daetools`::`massMatrixForm`

Extract mass matrix and right side of semilinear system of differential algebraic equations

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## Syntax

````MF` := daetools::massMatrixForm(`eqs`,`vars`)
```

## Description

`MF := daetools::massMatrixForm(eqs,vars)` returns a list containing the mass matrix `M` and the right side of equations `F` of a semilinear system of first-order differential algebraic equations (DAEs). Algebraic equations in `eqs` that do not contain any derivatives of the variables in `vars` correspond to empty rows of the mass matrix `M`.

The mass matrix `M` and the right side of equations `F` refer to the form `M(t,x(t)x'(t)) = F(t,x(t))`.

## Examples

### Example 1

Convert a semilinear system of differential algebraic equations to mass matrix form.

Create the following system of differential algebraic equations. Here, `x1(t)` and `x2(t)` represent state variables of the system. The system also contains symbolic parameters `r` and `m`, and the parameter `f(t, x1(t), x2(t))`.

```eqs := [m*x2(t)*diff(x1(t), t) + m*t*diff(x2(t), t) = f(t, x1(t), x2(t)), x1(t)^2 + x2(t)^2 = r^2]; vars := [x1(t), x2(t)];```
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Find the mass matrix form of this system.

```MF := daetools::massMatrixForm(eqs, vars): M := MF; F := MF```
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## 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 list of two matrices. The first entry is the mass matrix. The number of rows is the number of equations in `eqs`, and the number of columns is the number of variables in `vars`. The second entry is an `n`-by-`1` matrix of the right side of equations, where `n` is the number of equations `eqs`.

#### Mathematical Modeling with Symbolic Math Toolbox

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