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## Homework Statement

Using the values

**1**,

**0**, and

*****(to represent any number), list all the possible combinations that could result from performing reduced row echelon form on a 2 x 3 matrix.

## Homework Equations

Instructor 2 x 2 matrix example:

## The Attempt at a Solution

I have found 13 different combinations:

but we have no examples beyond the 2 x 2 matrix so I haven't been able to attempt to model an equation(since I can't find a theorem or definition that models this) to predict the number of combinations I should find for a 2 x 3 matrix.

Any help in determining if this is the correct amount of combinations for a 2 x 3 matrix that has been simplified to RREF or what ones I may be missing would be appreciated.