I am having trouble finding the general solution for this question:
Show that $a=(1,1,0)^T$ and $b = (-3,3,-2)^T$ are particular solutions to the system $\begin{bmatrix}2&-1&-5\\ 1&-4&-6\\ 3&2&-4 \end{bmatrix}X=\begin{bmatrix}1\\-3\\5\end{bmatrix}$ and find the general solution.
The book says the general solution is
$\begin{align}X & = a && + t(b-a) \\&= (1,1,0)^T && + t(-4,2,-2)^T\end{align}$
but how did they get that as the general solution?