Matlab solves linear systems

The system of algebraic equations
\[ {\bf A} \, {\bf x} = {\bf b} , \]
where A is a given matrix and b is specified column vector, may have a unique solution x, may have infinite many solutions, or may gave no solution at all. Another convenient way, and one that is computationally different is to type A\b, which is roughly the same as inv(A)*b. So if one wants to solve the system of equations Ax=b, it is enough to type 
			x=A\b
Numerical Methods
The condition number of an invertible matrix A is defined to be
\[ \kappa ({\bf A}) = \| {\bf A} \| \, \| {\bf A}^{-1} \| . \]
This quantity is always bigger than (or equal to) 1. We must use the same norm twice on the right-hand side of the above equation. Sometimes the notation is adjusted to make it clear which norm is being used, for example if we use the infinity norm we might write
\[ \kappa_{\infty} ({\bf A}) = \| {\bf A} \|_{\infty} \, \| {\bf A}^{-1} \|_{\infty} . \]
Applications