Final answer:
To solve the system of equations using matrices, represent the equations in matrix form and use matrix operations to find the solution.
Step-by-step explanation:
To solve the system of equations using matrices, we can represent the equations in matrix form and then use matrix operations to find the solution.
First, we write the system of equations in matrix form as:
[1 -1 0][x] = [2]
[3 0 -2][y] = [9]
[0 3 6][z] = [3]
Next, we can find the inverse of the coefficient matrix [1 -1 0; 3 0 -2; 0 3 6] and multiply it with the right-hand side matrix [2; 9; 3] to solve for the variables x, y, and z
After performing the necessary matrix operations, we find that x = 1, y = 2, and z = -1.