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

Determinant online

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

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.

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]]`).

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.

See also :

- Determinant : determinant. The determinant function calculates online the determinant of vectors or the determinant of a matrix.
- Inverse matrix calculator : inverse_matrix. The inverse_matrix function allows to calculate online the inverse of a matrix.
- Matrix calculator : matrix_calculator. The matrix calculator allows to do calculations with matrices online.
- Difference between two matrices : matrix_difference. The matrix calculators allows to calculate online the difference between two matrices with step calculations.
- Product matrix calculator : matrix_product. This matrix calculator allows to calculate online the product of two matrix with calculation step.
- Sum matrix calculator : matrix_sum. This matrix calculator allows to calculate online the sum of two matrix with calculation step.
- Solve system of linear equations : solve_system. The solve_system function allows to solve equations with several unknowns: Equation 2 unknown systems, systems of equations with 3 unknown in n unknowns systems.
- Trace of a matrix : trace. The matrix calculator calculates online the trace of a matrix. The trace of a square matrix is equal to the sum of the terms of its diagonal.
- Transpose matrix calculator : transpose_matrix. The matrix calculator allows to calculate online the transpose of a matrix.