(New page: =Inverse of a Matrix= Consider the <math>n</math>x<math>n</math> matrix <math>A</math>. The inverse of <math>A</math> is defined as <math>A^{-1}</math> such that <math>AA^{-1} = A^{-1}A=I_...) |
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Revision as of 06:11, 17 February 2010
Inverse of a Matrix
Consider the $ n $x$ n $ matrix $ A $. The inverse of $ A $ is defined as $ A^{-1} $ such that $ AA^{-1} = A^{-1}A=I_n $ where $ I_n $ is the identity matrix.
For example let
$ A= \begin{bmatrix} 1 & 4 \\ 1 & 3 \end{bmatrix} $
Then the inverse of A is
$ A^{-1} = \begin{bmatrix} -3 & 4 \\ 1 & -1 \end{bmatrix} $
