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 $r_2 \leftrightarrow r_3$.

row-switching

...

2. Multiplying a row by a nonzero number:

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

row-multiplication

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

 

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

row-addition

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.

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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.

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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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