Let Q be an infinitesimal generator: $$Q= \begin{pmatrix} -1 & 1 & 0&0&0&0 \\ 0 & -2 & 2 &0&0&0 \\ 0 & 0 & -3&3&0&0 \\ 0&0&0&-4&-4&0 \\ 0&0&0&0&-5&5 \\ 6&0&0&0&0&-6 \end{pmatrix} $$ Calculate the stationary probability distribution of the CTMC from the stationary distribution of its embedded MC.
If I am correct, the embedded MC is in this case $$W= \begin{pmatrix} 0 & 1 & 0&0&0&0 \\ 0 & 0 & 1&0&0&0 \\ 0 & 0 & 0&1&0&0 \\ 0 & 0 & 0&0&1&0 \\ 1 & 0 & 0&0&0&0 \\ \end{pmatrix} $$, since the probabilities of remaining in states (diagonals) are 0. Now I probably need to find an invariant vector but I am not sure how to do it.