Row operations (with example)

January 4, 2008

There are three kinds of row operations. Actually, there is some redundancy here – you can get away with two of them.

1. Swapping two rows:

Here is a swap of rows 2 and 3. I’ll denote it by $r_2 \leftrightarrow r_3$.



2. Multiplying a row by a nonzero number:

Here is row 2 multiplied by $\pi$. I’ll denote this operation by $r_2 \rightarrow \pi r_2$.


3. Adding a multiple of a row to another row:


I’ll subtract 4 times row 1 from row 2. Notation: $r_2 \rightarrow r_2 - 4r_1$.


Notice that row 1 was not affected by this operation. Likewise, if you do $r_{17} \rightarrow, row 17 changes and row 31 does not.


Matrices can be used to represent systems of linear equations. Row operations are intended to mimic the algebraic operations you use to solve a system.


One Response to “Row operations (with example)”

  1. […] I’ll do matrix row operation to convert the left-hand side of the double-wide into the identity. (As always with row operations, […]

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