„Erweiterte Matrix“ – Versionsunterschied

 

 

Let ''C'' be the square 2×2 matrix

:<math>

the right part of which is the inverse of the original matrix.

 

 

Consider the system of equations

In this example the coefficient matrix has rank 2 while the augmented matrix has rank 3; so this system of equations has no solution. Indeed, an increase in the number of linearly independent rows has made the system of equations '''inconsistent'''.

 

As used in linear algebra, an augmented matrix is used to represent the [[coefficients]] and the solution vector of each equation set.

For the set of equations