Line 8: Line 8:
 
<br>
 
<br>
 
<math>A = \left(\begin{array}{cccc}4&3\\3&2\end{array}\right)</math>  
 
<math>A = \left(\begin{array}{cccc}4&3\\3&2\end{array}\right)</math>  
<math>A<sup>-1</sup>\left(\begin{array}{cccc}-2&3\\3&-4\end{array}\right)</math>   
+
<br>
 +
<math>A^-1\left(\begin{array}{cccc}-2&3\\3&-4\end{array}\right)</math>   
  
 
<h3> Theorem 1 </h3>
 
<h3> Theorem 1 </h3>

Revision as of 06:54, 10 December 2012

Inverse of a Matrix

An n x n matrix A is said to have an inverse provided there exists an n x n matrix B such that AB = BA = In. We call B the inverse of A and denote it as A-1. Thus, AA-1 = A-1A = In. In this case, A is also called nonsingular.


Example.

$ A = \left(\begin{array}{cccc}4&3\\3&2\end{array}\right) $
$ A^-1\left(\begin{array}{cccc}-2&3\\3&-4\end{array}\right) $

Theorem 1

The inverse of a matrix, if it exists, is unique

Theorem 2

If A and B are both nonsingular n x n matrices (i.e. invertible), then AB is nonsingular and (AB)-1 = B-1A-1.

Alumni Liaison

Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett