H = (123 11 1 2 4 6 ) ; J = (2 4 2 1 6 1 29 2) ; K = (1 2 3 0 1 1 2 5 0 ) %3D

The objective is to find the determinant for $H=\left(1 2 3 1 1 1 2 4 6\right)$, $J=\left(2 4 2 1 6 1 2 9 2\right)$ and $K=\left(1 2 3 0 1 1 2 5 0\right)$.

The determinant of $H=\left(1 2 3 1 1 1 2 4 6\right)$ is,

$\begin{array}{rcl}H& =& \left|\left[\begin{array}{ccc}1& 2& 3\\ 1& 1& 1\\ 2& 4& 6\end{array}\right]\right|\\ & =& 1(6-4)-2(6-2)+3(4-2)\\ & =& 2-4+6\\ & =& 4\end{array}$

The determinant for $J=\left(2 4 2 1 6 1 2 9 2\right)$ is,

$\begin{array}{rcl}J& =& \left|\begin{array}{ccc}2& 4& 2\\ 1& 6& 1\\ 2& 9& 2\end{array}\right|\\ & =& 2(12-9)-4(2-2)+2(9-12)\\ & =& 6-6\\ & =& 0\end{array}$