AN INTRODUCTION TO ELEMENTARY ROW OPERATIONS Tools to Solve Matrices

What Are Elementary Row Operations?  There are three: 1. Row switching 2. Row multiplication 3. Row addition  They are used in Gaussian Elimination, a technique used to solve systems of linear equations that have been expressed as an augmented matrix.

Row Switching  Any two rows in a matrix can be switched.  All that changes is their relative positions within the matrix.  Written R i ↔ R j (i and j are row numbers).  Example:

Row Multiplication  Any row in a matrix can be multiplied by a nonzero constant.  Each number in that row is multiplied by that constant.  Written kR i → R i, where i is the row number and k is a nonzero constant.  Example:

Row Addition  Any row in a matrix can be replaced by the sum of that row and a multiple of another row.  The other row is unchanged.  Written R i + kR j → R i where k is a nonzero constant.  Example: