Systems of Linear Equations
A system of linear equations is said to be in row echelon form if its augmented matrix is in row echelon form. Similarly, a system of equations is said to be in reduced row echelon form or canonical form if its augmented matrix is in reduced row echelon form.
The canonical form may be viewed as an explicit solution of the linear system. In fact, the system is inconsistent, if and only if one of the equations of the canonical form is reduced to 1 = 0. Otherwise, regrouping in the right hand side all the terms of the equations, but the leading ones expresses the variables corresponding to the pivots as constants or linear functions of the other variables, if any.
Read more about this topic: Row Echelon Form
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