Cofactor Formula with Problem Solution & Solved Example

Cofactor Formula

If you ever used blinders then you must be sure how to create a cofactor? Blinders prevents you looking at other sides but you should focus what is available in front of you. In case of mathematics, cofactor is used to find the matric inverse, adjoined. A cofactor is the count you will get once a specific row or column is deleted from the matrix.

In simple words, this is just a numeric grid either in the form of a square or rectangle. There was always some sign is added before the cofactor value either positive or negative based on the position of element. To calculate the cofactor value of a matrix first you should find determinant of the minor and apply the same to the cofactor formula.

Cofactor expansions are popular when you wanted to compute determinant of a matrix having unknown identities. However, this is not possible reducing rows in this case because no one is sure either the contained entry is pivot or not.

Cofactor Formula

\[\ A_{ij}=(-1)^{i+j}\; \det\;M_{ij}\]

You could use combination of multiple techniques together to compute the determinant of a matrix. When you are planning to expand the cofactors on a matrix, you can always compute the determinants of cofactors in most convenient manner.

One can also delete row or columns. So, you can see that there are several techniques for calculating the determinant of a matric but combination is always the best solution instead of trying some technique alone. Remember that all computing techniques yield the same number.