This linear algebra tool performs Gaussian elimination, while generating an explanation of every step. For rational inputs, the answer is exact, in contrast with most numerical software.
Please enter your matrix in Matlab format, like in the example below:
[ 1 1.000001 1 ; 0.999999 1 0.999995]Without the heuristic, the program would find a pivot in the last column and declared the system inconsistent. With the heuristic, the program finds that the system has rank 1 (1 basic variable) and finds this reduced row echelon form:
[ 1 1.000001 1 ; 0 1 0 ]This is most likely what we want. In one case, when the entries are rational numbers (fractions), one should set the pivot threshold to 0 if the program starts replacing non-zero entries with zeros (unlikely for typical "book" examples).