b
(b) $\left| {\,\begin{array}{*{20}{c}}{3x - 8}&3&3\\3&{3x - 8}&3\\3&3&{3x - 8}\end{array}\,} \right| = 0$
${C_1} \to {C_1} + {C_2} + {C_3}$, we get
==> $(3x - 2)\left| {\,\begin{array}{*{20}{c}}1&3&3\\1&{3x - 8}&3\\1&3&{3x - 8}\end{array}\,} \right| = 0$
${R_1} \to {R_1} - {R_2}$and ${R_2} \to {R_2} - {R_3}$, we get
==> $(3x - 2)\left| {\,\begin{array}{*{20}{c}}0&{ - 3x + 11}&0\\0&{3x - 11}&{ - 3x + 11}\\1&3&{3x - 8}\end{array}\,} \right| = 0$
$\Rightarrow$ $(3x - 2)\left[ {{{( - 3x + 11)}^2}} \right] = 0$
$\Rightarrow\,x = \frac{2}{3}$ or $x = \frac{{11}}{3}\,\,\,\, \Rightarrow x = \frac{2}{3},\frac{{11}}{3}$.