<<VilGebra`

RowReduceQ[(({{1, 0, 0, 0}, {0, 1, E, 0}, {0, 0, 1, (Sqrt[2])}, {0, 0, 0, 0}}))]
RowReduceQ[(({{0, 0, 1, 0, 0, 1/2}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 8}, {0, 0, 0, 0, 0, 0}}))]