What are the value of k for which the system of equations:
(3k - 8)x + 3y + 3z = 0
3x + (3k - 8)y + 3z = 0
3x + 3y + (3k - 8)z = 0
has a not-trivial solution?

A. \[{\text{k}} = \frac{2}{3},\,\frac{{11}}{3},\,\frac{{10}}{3}\]

B. \[{\text{k}} = \frac{2}{3},\,\frac{{10}}{3},\,\frac{{11}}{3}\]

C. \[{\text{k}} = \frac{{11}}{3},\,\frac{{11}}{3},\,\frac{{11}}{3}\]

D. \[{\text{k}} = \frac{2}{3},\,\frac{{11}}{3},\,\frac{{11}}{3}\]

Answer: Option D