(New page: <br> == '''Inverse of a Matrix''' == ---- Definition: Let A be a square matrix of order n x n(square matrix). If there exists a matrix B such that A B = I n = B A Then B is ca...) |
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| − | *(AB)^-1 | + | *(AB)^-1 = B<span class="texhtml"><sup> − </sup>1</span> |
| − | <br> <br> <br> <math>\left(\begin{array}{cccc}1&2&3&4\\5&6&7&8\end{array}\right)</math> | + | <br> <br> <br> <br> <math>\left(\begin{array}{cccc}1&2&3&4\\5&6&7&8\end{array}\right)</math> |
Revision as of 10:19, 11 December 2011
Inverse of a Matrix
Definition: Let A be a square matrix of order n x n(square matrix). If there exists a matrix B such that
Then B is called the inverse matrix of A.
Conditions
A n x n is invertible (non-singular) if:
- Ax=0 has a unique solution
- There is a B matrix such that A B = In
- Ax=b has a unique solution for any b---x=A^-1 b
Properties
- (AB)^-1 = B − 1
$ \left(\begin{array}{cccc}1&2&3&4\\5&6&7&8\end{array}\right) $
