Summary On Determinants of Matrices of Order 2 and 3
- Let A be square matrix with order n. then determinant of A is a scalar value of a function of entries of A. The determinant of A is denoted by: $det(A)$ or $|A| \in \mathbb{R}$
- Let $A = \begin{pmatrix}
a_{11} & a_{12} \\
a_{21} & a_{22}
\end{pmatrix}$ be as quare matrix of order2 or (a 2 X 2 matrix),then determinant of A is defined as: $det(A) = |A| = a_{11} a_{22} – a_{12}a_{21}$ - Let $A = (a_{ij})_{n}$ be a matrix , where $n \in \mathbb{Z^+}$ and M be the sub matrix obtained by deleating $i^{th}$rows and $j^{th}$ column of A.
- hen :i). The minor of A at (i,j) is $M_{ij}(A)$ is the determinant of sub matrix $A_{ij}$. i.e. $M_{ij} = det(A_{ij})$
- ii). the cofactor $C_{ij}(A)$ is the sighned determinant of the sub matrix $A_{ij}$. i.e $C_{ij} = (-1)^{i+j}M_{ij}$.
