Question

Use matrix inversion to solve the system of linear equations.

−x − 4y + 2z = 22
x − z = 2
x + y − z = 4
(x, y, z) =

A. (-2, 8, 6)
B. (4, -2, 8)
C. (2, 3, 5)
D. (1, -3, 2)

Answer 1

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.