Matrix Inversion

Saturday, 9 June 2018

3:25 PM

Not all matrices have an inverse!

 

A matrix X is an inverse of A if both  and , where  is the identity matrix

 

If a matrix invertible it is also called non-singular

 

Conditions for a Matrix to be Invertible

• Matrix is a square (size of )

 

Matrix Operations

• 
• 
• 
• 
  
  
   

 

(actually) Finding the inverse of a matrix

Consider the matrix

The identity matrix I of size  is



• Reduce to reduced row-echelon form - effectively make A into I

 



 





 





 





 





 

Therefore



 

 

 

 

 

 

Inverse of a matrix

 

• Augment A and its identity matrix
• Then perform row operations until A is also equal to its identity matrix

 

Finding the determinant of  by

• If
• If  exists
• If  has c solutions for every c