Presentations

Hello

Description
There are many useful applications of the determinant. Cofactor expansion is one technique in computing determinants.
Categories
Published
of 7
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Related Documents
Share
Transcript
  Hello There are many useful applications of the determinant. Cofactor expansion is one technique in computing determinants. Now, we discuss how to find these cofactors through minors of a matrix and use both of these elements to find the adjoint of A. Then by the adjoint and determinant, we can develop a formula for finding the inverse of a matrix. Minors: To find the minors of any matrix, expand block out every row and column one at a time until all the minors are found. Steps to Finding Each Minor Of A Matrix: 1. Delete the i th row and j th column of the matrix. 2. Compute the determinant of the remaining matrix after deleting the row and column of step 1. Example: Find the minors of the matrix              1 1 1 2 1 1 1 1 2 . *Note: This step procedure just outlines finding the minor M 11 of the matrix. 1. Delete the i th row and j th column of the matrix.              1 1 1 2 1 1 1 1 2 2. Compute the determinant of the remaining matrix after deleting the row and column of step 1. ( 1)( 1) (1)(1) 0  1 1 1 1 det 1 1 1 2 1 1 1 1 2 11                            M Using the same steps above, the other minors of the matrix are given below. 3 1 1 2 1 det 12         M  3 1 1 2 1 det 13         M  1 1 1 1 2 det 21          M  3 1 1 1 2 det 22         M  2 1 1 1 1 det 23        M  1 1 1 1 2 det 31         M   3 2 1 1 2 det 32        M  1 2 1 1 1 det 33         M  Thus, the minor matrix is given by                1 3 1 1 3 2 0 3 3 M Cofactors: To find the cofactors of a matrix, just use the minors and apply the following formula: C ij = (-1) i + j M ij where M ij is the minor in the i th row, j th position of the matrix. Example: Find the cofactors of the matrix     

Cyberpower

Jul 23, 2017

sdcs-01

Jul 23, 2017
We Need Your Support
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks