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[tex] \left[\begin{array}{ccc}1&1&1\\1&1&-1\\1&-1&1\end{array}\right] \, \left[\begin{array}{ccc}x\\y\\z\end{array}\right] \, = \left[\begin{array}{ccc}0\\-2\\4\end{array}\right] \\ Det\, D\,= 1(0) -1(2) + 1(-2) = -4\\ Det\' X\,= 0(2) - 1(2) + 1(-2) = -4\\ Det\,Y\,= 1(2) - 0(2) + 1(6) = 8\\ det\,Z\,= 1(2) - 1(6) + 0(-2) = -4\\ x = -4/-4 = 1 \\ y = 8/-4 = - 2 \\ z = -4/-4 = 1\\ (x,y,z)\.=(1, -2, 1)[/tex]\\