## `student::isFree` -- test for linear independence of vectors

#### Introduction

`student::isFree`(`S`) tests if the vectors given in `S` are linear independend.

#### Call(s)

`student::isFree(S)`

#### Parameters

`S` | - | set or list of vectors (of category `Cat::Matrix`) defined over a `Cat::Field`)

#### Returns

either `TRUE` or `FALSE`.

#### Related Functions

`linalg::basis`

#### Details

- `student::isFree`(`S`) gives `TRUE` if `S` is free, i.e. the vectors of `S` are linear independend. Otherwise the value `FALSE` is returned.

#### Example 1

We define 3 vectors:

    >> x := matrix( [[2,3,4]] ):
       y := matrix( [[1,-1,1]] ):
       z := matrix( [[2,3,5]] ):

And we ask if x, y and z are linear independend.

    >> student::isFree( {x,y,z} )

                                       TRUE

Hence, the vectors x,y,z are linear independent, and therefore the set x,y,z is a basis of R^3 Of course the vectors x,y and (x-y) are not linear independent:

    >> student::isFree( [x,y,x-y] )

                                       FALSE

If we have vectors from different vector spaces, `student::isFree` will give an error message:

    >> zz := matrix( [[2,3,5,6]] ):
       student::isFree( {x,y,zz} )

          Error: set contains incompatible vectors [student::isFree]

#### Changes

- no changes

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