## 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.

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**1. Swapping two rows:**

Here is a swap of rows 2 and 3. I’ll denote it by .

...

**2. Multiplying a row by a nonzero number:**

Here is row 2 multiplied by . I’ll denote this operation by .

…

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

I’ll subtract 4 times row 1 from row 2. Notation: .

Notice that row 1 was *not* affected by this operation. Likewise, if you do , 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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January 5, 2008 at 10:14 pm

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