Inverse of a Matrix
Matrix Inverse
Multiplicative Inverse of a Matrix
For a square matrix A, the inverse is written A-1. When A is multiplied by A-1 the result is the identity matrix I. Non-square matrices do not have inverses.
Note: Not all square matrices have inverses. A square matrix which has an inverse is called invertible or nonsingular, and a square matrix without an inverse is called noninvertible or singular.
AA-1 = A-1A = I
Example: | ![]() ![]() |
and A-1A = |
Here are three ways to find the inverse of a matrix:
1. Shortcut for 2x2 matrices For |
Example: |
Use Gauss-Jordan elimination to transform |
Example: The following steps result in |
so we see that |
3. Adjoint method A-1 = |
Example: The following steps result in A-1 for The cofactor matrix for A is
|
See also
Copyrights © 2013 & All Rights Reserved by ayotzinapasomostodos.comhomeaboutcontactprivacy and policycookie policytermsRSS