The provided matrix has no solution.
Work Step by Step
In this matrix, it is impossible to convert the last matrix to the desired form of 1st down the main diagonal. Translating row 3 of the matrix into equation form, we get, $0x+0y+0z=-27$ There are no values of x, y and z for which $0=-27$ This is false, regardless of any values for x, y, z. Thus the last equation can never be a true statement and there is no solution.