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--- elementary_row_operation [2015/01/27 12:18] – rupert
+++ elementary_row_operation [2015/03/26 10:12] (current) – rupert
@@ Line 1: / Line 1: @@
-Recall that when we form the augmented matrix of a linear system, each equation in the system becomes a row of the matrix. So we can translate the elementary operations of the linear system into corresponding operations on the rows of the matrix. We get three different types:
+Recall that when we form the [[augmented matrix]] of a linear system, each equation in the system becomes a row of the matrix. So we can translate the [[elementary operations on a linear system|elementary operations on the linear system]] into corresponding operations on the rows of the matrix. We get three different types:
   - change the order of the rows of the matrix;
   - multiply one of the rows of the matrix by a non-zero real number;
-  - replace row $j$ by row $j$ ${}+{}$ $c\times {}$ row $i$, where $c$ is a non-zero real number.
+  - replace row $j$ by "row $j$ ${}+{}$ $c\times {}$ (row $i$)", where $c$ is a non-zero real number and $i\ne j$.
 The system of linear equations corresponding to these matrices will then have exactly the same solutions.
-We call these operations **elementary row operations** on the matrix.
+We call these operations **elementary row operations** or **EROs** on the matrix.