Understanding Cofactor & Adjugate Matrices

[TimeRip496]

Can anyone explain to me what is the cofactor matrix? I have trouble finding on the net the intuition behind it. Likewise what is the meaning of the adjugate matrix?

 

[Matterwave]

This is a lesson in linear algebra. Probably it would be good to consult your linear algebra book about this for a thorough understanding.

A cofactor matrix is a matrix whose entries are the cofactors of some other matrix. While the adjugate matrix is simply the transpose of the cofactor matrix.

Hopefully you learned how to take co-factors when finding determinants. The cofactor of some entry $A_{ij}$ in a matrix $\bf{A}$ is the determinant of the resulting matrix when you delete the ith row and j'th column of the matrix $\bf{A}$ and then accounting for an alternating sign, a factor of $(-1)^{i+j}$.