determinant calculator

The determinant calculator allows to find determinants online. The calculator can calculate determinant of two vectors , determinant of three vectors or determinant of matrix .

Determinant of two vectors (determinant 2x2)

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.

• Calculation of determinant
1. `det((3,4/5),(1/2,2))=3*2-4/(2*5)=3*2-2/5=28/5`
2. `det((3,4/5),(1/2,2))=28/5`

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.

• Calculation of determinant
1. `det((a,3*a),(b,2))=a*2-b*3*a=2*a-3*b*a`
2. `det((a,3*a),(b,2))=2*a-3*b*a`

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

Determinant of three vectors(determinant 3x3)

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]]).

• Calculation of determinant
1. `det((3,3),(1,2))=3*2-3=3`
2. `det((3,3),(1,2))=3`
3. `det((3,3,4),(1,2,0),(0,1,7))=25`

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]]).

• Calculation of determinant
1. `det((3,3),(1,2))=3*2-3=3`
2. `det((3,3),(1,2))=3`
3. `det((3,3,4),(1,2,1),(0,1,2))=7`