Why can't my graphing calculator find the RREF of the transpose of a matrix?

Question

I know this is somewhat of an odd question, but I am having trouble with my TI-84 calculator and I don't know why.

I'm trying to find the RREF of the transpose of a $4\times6$ matrix; for some reason my graphing calculator gives me an error. Something to do with the dimensions? Here is a photo of matrix $A$.

I want to find RREF$(A$ transposed$)$.

Answer 1

The TI-84's rref function throws an error if there are more rows than columns, and the transpose has more rows than columns.

Answer 2

Change your matrix from 6x4 to 6x6 by adding two columns of zeros. Then you can use the rref or ref functions. Then just ignore the added columns.

Answer 3

To compute a unique solution for a system of equations you need the same number of equations as unknowns. In other words if you have 4 variables (unknowns) you need only 4 equations.

Adding more equations than variables creates what is called an "over determined" system of equations. In most "math class" type problems, all you need to do is drop 2 equations and solve using the remaining 4 equations. It does not matter which two equations you drop (although common sense would say to drop the more complex equations).

There is a field of "applied" math in which we intentionally write more equations than variables. This is usually done when the numerical data contains small measurement errors. Using an "over determined" system of equations allows you to compute the most statistically likely answer for each variable.