how to solve this? As the rows are dependent I only get 2x+y-3z=0. What am I supposed to do from here? I have no other idea then guessing solutions. I know the solution is this but I don't get how I should calculate it from the point 2x+y-3z

Two of the variables are free. For instance set b = r and c = s, and solve for a in terms of those parameters.

That’s the general solution. Then what’s left is to write it in the form of vectors and the parameters r and s.
You actually get an entire plane of solutions. If you let y=lambda, z=mu then you should be able to write (x,y,z) in terms of lambda and mu the manipulate this so that it can easily be seen it’s a plane.

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