Math 2.0

Linear and multilinear algebra; matrix theory Definition

Elementary row operations

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Definition

Let FF be a field and let AA be an m×nm \times n matrix over FF, with rows R1,…,RmR_1, \dots, R_m. An elementary row operation on AA is one of these three operations:

  1. Row switching: exchange RiR_i and RjR_j for some i≠ji \ne j.
  2. Row scaling: replace RiR_i by cRic R_i for some c∈Fc \in F with c≠0c \ne 0.
  3. Row addition: replace RiR_i by Ri+cRjR_i + c R_j for some i≠ji \ne j and some c∈Fc \in F.

Remarks

Each elementary row operation has an inverse operation of the same type. Each elementary row operation on AA is the same as the product EAEA for an elementary matrix EE. Elementary row operations on an augmented matrix do not change the solution set of the system. Elementary column operations have the same definition with columns in place of rows.

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Further reading

  1. Web https://en.wikipedia.org/wiki/Elementary_matrix, Elementary row operations
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