Determinants
If A is a square matrix then the determinant function is denoted by det and det(A)
For an instance we have a 2 x 2 matrix denominated A, therefore:
det(A) = [a11 , a12 ; a21 , a22 ]
As we already defined the determinant function we can write some formulas. The formulas for any 2 x 2 and 3 x 3 matrix will be:
The determinant function for a 2 x 2 matrix is:
$ det(A)=\left(\begin{array}{cccc}a11&a12\\a21&a22\end{array}\right) $
= (a11 * a22) - (a12 * a21 )
The determinant function for a 3 x 3 matrix is:
$ det(A)=\left(\begin{array}{cccc}a11&a12&a13\\a21&a22&a23\\a31&a32&a33\end{array}\right) $
= (a11 * a22 * a33) + (a12 * a23 * a31) + (a13 * a21 * a32) - (a12 * a21 * a33) - (a11 * a23 * a32) - (a13 * a22 * a31)
Properties of Determinants
