Row Equivalence & Elementary Row Operations are materials for the course Introduction to Linear Algebra at the University.

❖ Two matrices \(A\) and \(B\) are Row Equivalent if it is possible to transform \(A\) into \(B\) by a sequence of Elementary Row Operations.

❖ Elementary row operations

There are three types of elementary matrices, which correspond to three types of row operations (respectively, column operations):

1. Row switching \(A\) row within the matrix can be switched with another row.

2. Row multiplication Each element in a row can be multiplied by a non-zero constant.

3. Row addition \(A\) row can be replaced by the sum of that row and a multiple of another row.