You may see a display like this in which it appears that the computer has made an arithmetic error.

What really transpired was more likely something like

This is because the row operations package uses some global variables
which are initialized by the start_ge() command. When making corrections,
one needs to **re-execute** all lines from the start_ge() on
down to get the correction properly interpreted. (This just means
putting your mouse somewhere and hitting execute a bunch of times ...)

The matrix must be in echelon (upper triangular) form before back substitution is invoked.

Here first swapping rows 1 and 2 makes the matrix appropriately triangular.

For matrices with floating point entries, small roundoff errors prevent ordinary back substitution from being used.

Use the rounded form instead. By default rounding is to 4 or 5 decimals.

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Last Update: * September 12, 1998*