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

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

The **determinant calculator** allows to find 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]]`).

determinant(matrix)

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

See also

- Vector calculator : vector_calculator. The vector calculator allows to do calculations with vectors using coordinates.
- Calculating the coordinates of a vector from two points. : vector_coordinates. The vector calculator allows the calculation of the coordinates of a vector from the coordinates of two points online.
- Determinant calculator : determinant. The determinant function calculates online the determinant of vectors or the determinant of a matrix.
- Calculating the difference of two vectors : vector_difference. The vector_difference function is used to calculate the difference of two vectors online.
- Calculating the norm of a vector : vector_norm. The vector calculator allows the calculation of the norm of a vector online.
- Calculus scalar triple product : scalar_triple_product. The scalar triple product calculator allows online calculation of scalar triple product.
- Dot product calculator : dot_product. The dot product calculator allows the calculation of the dot product of two vectors online from their coordinates.
- Product of a vector by a number : product_vector_number. The vector calculator allows to calculate the product of a vector by a number online.
- Cross product calculator : cross_product. The vector calculator allows the calculation of the cross product of two vectors online from their coordinates.
- Calculating the sum of two vectors : vector_sum. The vector calculator allows the calculation of the sum of two vectors online.