Wednesday, June 5

Inverting Matrices

The inverse of a square matrix A, sometimes called a reciprocal matrix, is a matrix   such that         
Where I is the identity matrix.
A square matrix A has an inverse if the determinant . A matrix possessing an inverse is called nonsingular, or invertible.
The matrix inverse of a square matrix m may be taken in mathematics using the function inverse[m].

Inverse of 2x2 Matrix


For a 2X2  matrix
A= `[[a,b],[c,d]]`
The matrix inverse is
                  
             =  

                   =    

Inverse of 3x3 Matrix


For a 3X3 matrix
          
The matrix inverse is


A general matrix can be inverted using methods such as the gauss Jordan elimination, Gaussian elimination.

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