If we have a problem where we know a solution to a R2 linear system, we were told something about the general solution involving a linear combination of the x and y coordinates?, but I'm a little stuck
Example: Give an example of a linear system for which (x,y) = (e^(−t) , α) is a solution for every constant α. Sketch the direction field for this system. What is the general solution of this system?
Any help appreciated!