Question

How do you do cofactor expansion?

Answer 1

Cofactor expansion of a matrix :

Let a matrix having order of $n\times n$ i.e. a square matrix $a_{ij}$where $i$ denotes row and $j$ denotes column and $i,j\in N$

$A=\left[\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}& a_{32}& a_{33}\end{array}\right]$

Formula of cofactor$C_{ij}={(-1)}^{i+j}{M}_{ij},wherei,jdenotesrowandcoloumn$

Then cofactor of a matrix is define as $C_{11}={(-1)}^{1+1}(a_{22}\times a_{33}-a_{23}\times a_{32})$ this is co factor for $a_{11}$

Similarly, $C_{12}={(-1)}^{1+2}(a_{21}\times a_{33}-a_{23}\times a_{31})$, similarly we can find cofactor for other.

Hence, we can find cofactor by using the above formula and applying the above method.