Question

Solve the system of equations using matrix equations:

3x + y + z = 5
x + 2y + z = 0
2x - y - 2z = -5
Which of the following values is part of the correct solution?
A. x = 2, y = -1, z = 3
B. x = 1, y = -2, z = 3
C. x = 0, y = 3, z = -5
D. x = -1, y = 4, z = 1

Answer 1

The correct solution to the given system of equations is x = 1, y = -2, z = 3 (Option B).

Step-by-step explanation:

The system of equations can be represented in matrix form as follows:

3x + y + z = 5

x + 2y + z = 0

2x - y - 2z = -5

In matrix form, AX=B, where:

A = [3 1 1; 1 2 1; 2 -1 -2]

X = [x; y; z]

B = [5; 0; -5]

Solving the matrix equation AX=B gives the solution X = [1; -2; 3], which corresponds to x = 1, y = -2, z = 3. Therefore, Option B is the correct solution.