When Gaussian Elimination Fails?

Gaussian elimination, as described above, fails if any of the pivots is zero, it is worse yet if any pivot becomes close to zero. In this case, the method can be carried to completion, but the obtained results may be totally wrong.

What method fails if any one of the pivot becomes zero?

Gauss elimination method fails if any one of the pivot elements becomes zero or very small. In such a situation we rewrite the equations in a different order to avoid zero pivots.

Can Gaussian elimination have no solution?

Thus, there is no solution. The first step is to get a 1 in the first row of the first column. Since there is a 1 in the second row, we'll do a row swap. The second step is to get zeros in the remaining cells of the first column.