Elimination matrix

The entire collection of all the simple row operations we perform to change a matrix into reduced row-echelon form can be brought together in one matrix, and we call that matrix the elimination matrix, (елементарна матрица).

Proof that is square §

Example §

Performing simple row operations on to get it to reduced row-echelon form:

Representing the row operations with matrices, using :

To get the elimination matrix, multiply :