Determinanți

Determinant de ordin 2:

Fie A o matrice pătratică de ordin 2. $A=\left(\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right)$

Determinantul matricei A este numărul detA:

$det\left(A\right)=\left|\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right|=a_{11}\cdot a_{22}-a_{12}\cdot a_{21}$

Determinant de ordin 3

Fie A o matrice pătratică de ordin 3: $A=\left(\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}& a_{32}& a_{33}\end{array}\right)$

Determinantul matricei A este numărul detA:

$detA=\left|\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}& a_{32}& a_{33}\end{array}\right|=a_{11}\cdot a_{22}\cdot a_{33}+a_{21}\cdot a_{32}\cdot a_{13}+a_{31}\cdot a_{12}\cdot a_{23}-$

$-\left(a_{13}\cdot a_{22}\cdot a_{31}+a_{23}\cdot a_{32}{a}_{11}+a_{33}\cdot a_{12}\cdot a_{21}\right)$