elementary row operations

transformations that can be done on a matrix, helpful in finding the reduced row echelon form of a matrix. These transformations include:
a) switching the order of the rows of the matrix
b) multiplying a row by a scalar
c) adding one row of the matrix to another row.

Any e.r.o. can also be written as an elementary matrix. The elementary matrix for an e.r.o. R₁ is found by applying R₁ to I (the identity matrix) .

If A -> B under an e.r.o. R₁, then
A.r = B,

where r is the elementary matrix corresponding to R₁.