Originally Posted by

**mr fantastic** I am stunned that you get a unique solution for the first system, since the matrix A corresponds to k = -2 and, in case the penny hasn't dropped yet, k = -2 makes the determinant equal to zero. Which means that there is NOT a unique solution. Either no solution or infinite solutions and you have to check which.

Again the cutting of corners .... Did you bother to check that x = 10, y = 5 and z = 4 satisfy

x - y - 2z = 7

2x - 2y - 2z = 2

x - y + 2z = 13

To seal the deal, I did. They do not (unsurprisingly).