LINEAR ALGEBRA

Use the determinant of the coefficient matrix to determine whether the system of linear equations has a unique solution.

2x₁ + 3x₂ + 3x₃ = 36x₁ + 6x₂ + 12x₃ = 1312x₁ + 9x₂ ? x₃ = 2

The system has a unique solution because the determinant of the coefficient matrix is nonzero.The system has a unique solution because the determinant of the coefficient matrix is zero. The system does not have a unique solution because the determinant of the coefficient matrix is nonzero.The system does not have a unique solution because the determinant of the coefficient matrix is zero.

If the system has a unique solution, use Cramer's Rule to find the solution. (If not possible, enter IMPOSSIBLE.)

(x₁, x₂, x₃) =

Use the determinant of the coefficient matrix to determine whether the system of linear equations has a unique solution. 2x1 + 3x + 3x3 = 3 6x + 6x + 12x3 = 13 12x1 + 9x2 - x3 = 2 O The system has a unique solution because the determinant of the coefficient matrix is nonzero. O The system has a unique solution because the determinant of the coefficient matrix is zero. O The system does not have a unique solution because the determinant of the coefficient matrix is nonzero. O The system does not have a unique solution because the determinant of the coefficient matrix is zero. If the system has a unique solution, use Cramer's Rule to find the solution. (If not possible, enter IMPOSSIBLE.) (x1, x2, x3) = =([