Examine the following system of linear equations and solve it, if possible:
x+y+z=6,
2x−y+3z=14,
3x+4y−2z=2.
(i) Form the matrices A, X, and B such that AX=B.
(ii) Compute ∣A∣.
(iii) Using the value of ∣A∣, comment on the nature of the solution of the system.
(iv) If the system is consistent with a unique solution, find the values of x, y, and z.