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) = [a11 , a12 ; a21 , a22]
= a11 * a22 - a12 * a21
The determinant function for a 3 x 3 matrix is:
det(A) = [a11 , a12, a13 ; a21 , a22 , a23 ; a31 , a32 , a33]
= (a11 * a22 * a33) + (a12 * a23 * a31) + (a13 * a21 * a32) - (a12 * a21 * a33) - (a11 * a23 * a32) - (a13 * a22 * a31)
$ <math>\left(\begin{array}{cccc}1&2&3&4\\5&6&7&8\end{array}\right) $</math>
