2. Resolva utilizando a Regra de Crammer (Determinante \[ \left\{\begin{array}{c} 3 x-2 y+z=6 \\ x+y-z=4 \\ 2 x+y-2 z=6 \end{array}\right. \]

Step 1 ：Find the determinants of the main matrix and the matrices obtained by replacing each column with the constants on the right side of the equations:

Step 2 ：\(D = \begin{vmatrix} 3 & -2 & 1 \\ 1 & 1 & -1 \\ 2 & 1 & -2 \end{vmatrix} = -4\)

Step 3 ：\(D_x = \begin{vmatrix} 6 & -2 & 1 \\ 4 & 1 & -1 \\ 6 & 1 & -2 \end{vmatrix} = -12\)

Step 4 ：\(D_y = \begin{vmatrix} 3 & 6 & 1 \\ 1 & 4 & -1 \\ 2 & 6 & -2 \end{vmatrix} = -8\)

Step 5 ：\(D_z = \begin{vmatrix} 3 & -2 & 6 \\ 1 & 1 & 4 \\ 2 & 1 & 6 \end{vmatrix} = -4\)

Step 6 ：Find the values of x, y, and z by dividing the determinants of the matrices with replaced columns by the determinant of the main matrix:

Step 7 ：\(x = \frac{D_x}{D} = \frac{-12}{-4} = 3\)

Step 8 ：\(y = \frac{D_y}{D} = \frac{-8}{-4} = 2\)

Step 9 ：\(z = \frac{D_z}{D} = \frac{-4}{-4} = 1\)

Step 10 ：\(\boxed{x = 3, y = 2, z = 1}\)