Final answer:
The solution to the system of linear equations by using matrix inversion is (4, -2, 8), corresponding to answer choice B.
Step-by-step explanation:
To solve the system of linear equations using matrix inversion, we first write the system in matrix form as AX = B, where A is the matrix of coefficients, X is the column matrix of variables (x, y, z), and B is the column matrix of constants from the right-hand side of the equations.
The system given is:
-x - 4y + 2z = 2
2x - z = 2
x + y - z = 4
The matrix form is:
A = -1 -4 2 2 0 -1 1 1 -1 , X = x y z , B = 2 2 4
Next, we find the inverse of matrix A (A-1) and multiply it by B to find X:
X = A-1B
After calculations, we get:
x = 4, y -2, z = 8
Therefore, the solution to the system of equations is (x, y, z) = (4, -2, 8), which corresponds to answer choice B.