Calculator will not find row reduced echelon form

Question

I have a TI-84 Plus CE which I am using to find the row reduced echelon form of matrices. It has worked well so far, but it gives me an "Invalid Dimension" error for this matrix: $$\begin{pmatrix}1 & 2\\\ 3 & 6\\\ 2&4\end{pmatrix}$$ Now it seems evident to me that the row reduced echelon form is $$\begin{pmatrix}1 & 2\\\ 0 & 0\\\ 0&0\end{pmatrix}$$ so why can my calculator not find this?

Answer 1

From http://tibasicdev.wikidot.com/rref:

The rref( command can be used to solve a system of linear equations. First, take each equation, in the standard form of $a_1x_1+\dots+a_nx_n=b$, and put the coefficients into a row of the matrix.

Then, use rref( on the matrix. There are three possibilities now:

• If the system is solvable, the left part of the result will look like the identity matrix. Then, the final column of the matrix will contain the values of the variables.
• If the system is inconsistent, and has no solution, then it will end with rows that are all 0 except for the last entry.
• If the system has infinitely many solutions, it will end with rows that are all 0, including the last entry.

ERR:INVALID DIM is thrown if the matrix has more rows than columns.

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One thing I'd recommend doing is just adding columns of $0$'s until you have a square matrix. Then, the program will row reduce as normal and you can ignore the extra columns.