Use the matrix D^-1= [[-23, -4, 6], [-8, -1, 2], [12, 2, -2]] to calculate the solutions of this system: x+2z=-2 3y+2z=8 4x+2y+9z=-4

To solve the system of equations using the inverse matrix D^-1, you can represent the system in matrix form as follows: Ax = b Where: A is the coefficient matrix of the system, x is the column vector of variables [x, y, z], b is the column vector of constants [−2, 8, −4], and D^-1 is the inverse matrix of A. The coefficient matrix A can be extracted from the equations as follows: A = [[1, 0, 2], [0, 3, 2], [4, 2, 9]] Now, you can solve for x by multiplying both sides of the equation by D^-1: x = D^-1 * b First, calculate D^-1 * b: D^-1 * b = [[-23, -4, 6], [-8, -1, 2], [12, 2, -2]] * [[-2], [8], [-4]] = [[(-23 * -2 + -4 * 8 + 6 * -4)], [(-8 * -2 + -1 * 8 + 2 * -4)], [(12 * -2 + 2 * 8 + -2 * -4)]] = [[46 - 32 - 24], [16 - 8 - 8], [-24 + 16 + 8]] = [[-10], [0], [0]] Now, you have the solution for x: x = [[-10], [0], [0]] So, the solutions to the system of equations are: x = -10 y = 0 z = 0