# determinant

## Calculus determinant

The determinant function calculates online the determinant of vectors or the determinant of a matrix.
determinant([[3;1;0];[3;2;1];[4;1;7]]), returns 22

### Function : determinant

#### Summary :

The determinant function calculates online the determinant of vectors or the determinant of a matrix.

determinant online

#### Description :

The determinant function calculates determinants online. The calculator can calculate determinant of two vectors , determinant of three vectors or determinant of matrix .

# Determinant of two vectors

In an orthonormal coordinate system (O,vec(i),vec(j)) , the vector vec(u) has coordinates (x,y) (vec(i),vec(j)), the vector vec(v) has coordinates (x',y'). The determinant of vec(u) et vec(v) is equal to the number xx'-yy'.

The calculator can calculate determinants giving exact results : to calculate the determinant of (3,1/2) and (4/5,2), enter determinant([[3;1/2];[4/5;2]]), after calculation, the result is returned.

The calculator allows for symbolic calculations, it is possible to use letters : to calculate a determinant of two vectors as follows : (a,b) et (3a,2), enter determinant([[a;b];[3a;2]]), after calculation, the result is returned.

Note: When the determinant of two vectors is zero, the two vectors are collinear.

# Determinant of three vectors

In an orthonormal coordinate system (O,vec(i),vec(j),vec(k)), the vector vec(u) has coordinates (x,y,z) , the vector vec(v) has coordinates (x',y',z'), the vector vec(k) has coordinates (x'',y'',z''). The determinant of vec(u), vec(v), vec(k) is equal to the number xy'z''+x'y''z+x''yz'-xy''z'-x'yz''-x''y'z.

To calculate a determinant of three vectors, use the following syntax : determinant([[3;1;0];[3;2;1];[4;0;7]]).

# Determinant of a matrix

The determinant calculator can be used on square matrices of order n, it is also able to do symbolic calculations. To calculate a matrix determinant, use the following syntax : determinant([[3;1;0];[3;2;1];[4;1;2]]).

The determinant function calculates online the determinant of vectors or the determinant of a matrix.

#### Syntax :

determinant(matrix)

#### Examples :

determinant([[3;1;0];[3;2;1];[4;1;7]]), returns 22

Calculate online with determinant (determinant)