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## Solvability of Linear Systems of Equations and Matrix Inversion with MATLAB |

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z | overview |

A linear system can be solved in MATLAB with the command `
x=A \b`.

Depending on the dimensions different techniques are used.

- If
`A`is an matrix, then the system is solved by means of Gaussian elimination. - If
`A`is an matrix with , then the approximate solution of the overdetermined or underdetermined system of equations is calculated by a least square procedure minimizing .

In case of numerically instable matrices or in case of systems with loss
of rank a warning will be displayed. (The matrix is close to singular or badly
scaled.)

The MATLAB function `inv` inverts a regular square matrix:

`\`

b`\`

-command
uses more efficient and more stable algorithms.
Finally,

automatically generated 3/ 8/2007 |