I have a question that asks to draw the direction field for the set of linear systems.
$\begin{align} \frac{d\,x}{dt} &= -x + y + 1 \\ \frac{d\,y}{dt}&=x+y+3\end{align}$
My attempt:
What I did first was set the system in the form of $d(Q)/dt = KQ + b$, then I found the critical points which was at $[2,1]$ and then I chose an arbitrary point in the plane, lets pick $[1,2]$, and set it as my Q and then solved and found the vector $[1,3]$ to be associated to that point, but this is where I have a problem. How will this vector be plotted? I am on point $[1,2]$ and the tangent vector is $[1,3]$ but how can I draw this? Will it go up 1 unit and right 3?