Final answer:
To solve the system of equations using the matrix method, we need to represent the equations in matrix form and find the inverse of the coefficient matrix. Then, we multiply the inverse with the constant matrix to get the values of x, y, and z. Therefore, x = 2, y = 1, and z = 1.
Step-by-step explanation:
To solve the system of equations using the matrix method, we first need to represent the equations in matrix form.
The given system of equations is:
3x - 2y + 3z = 8
2x + y - z = 1
4x - 3y + 2z = 4
Writing the coefficients of the variables in a matrix, we get:
[3 -2 3; 2 1 -1; 4 -3 2]
Now, we need to find the inverse of the coefficient matrix and multiply it with the constant matrix [8; 1; 4].
Multiplying the inverse with the constant matrix gives us the values of x, y, and z. Therefore, x = 2, y = 1, and z = 1.