Co factors of a matrix and Cramer's rule - Method of solving

Co-factor of a matrix

There are 2 methods, which are simple, to find a co factor matrix:

1.Long method

2.Short method

The long method

Assume that we are considering a 2*2 matrix named A.

The above is the method to find the co factors of a 2*2 matrix. We can use the same method to find the cofactor matrix for a 3*3 matrix too. 

The short cut method

For a better understanding we consider a 3*3 matrix and we name it A.

Now we have to find the determinants of each aligned semi matrices and the result would be the co cofactor matrix.

Cramer's rule

We can find the values of the variables using the Cramer's rule, where we'll have to use the linear equations to find out the answer;

For a better understanding of the method let’s consider a 2*2 matrix; and hence 2 linear equations would be given: