Determine whether the set $\{v_1 + v_2 - v_3, 2v_1 + 2v_3, -v_1 + v_2 - 3v_3\}$ is linearly dependent or independent. We had a question on our last test that was very similar to this and I only got $2$ points of $6$ and I want to make sure I do it right this time. Here's my solution to that one: 
Let $v_1, v_2,$ and $v_3$ be three linearly independent vectors. 
My teacher told me that to qualify for full credit every detail of my suloution must be presented and the logical steps that lead to my conclusion must be clear, justified, and readable. 
Here's what my solution would be to the question, but i don't think it's enough. 
Here's my updated solution, this should be enough right? 
Thanks guys

If one understands why you came up with the original matrix and how the linear dependence follows from your fast reasoning and writings derived from that matrix, then it's fine. However, to make a proof that is unquestionable, you would probably need more detail. However, if it makes you feel any better, if I were a professor I would be inclined to give you credit for correct intentionality based on what you wrote and I would give you full credit. Time is short on tests, after all.
