Need some help with a linear transformation problem.

[emmanck123]

I already have most of the exercise finished, I just need help finding the image of the L.T. The way my teacher thought us to solve the problem is by solving the matriz by the Gauss Jordan method and then we take the free variables as our parameters for finding the null space and image. Sorry if I cant explain myself too well, it's faster by showing what I have done so far. If theres a better way or diferent method to solve it, i'll happly do it.

 

[Steven G]

Why did you stop where you did? Just like the reducing before you still one more row operation to preform! Finish up and post back if you need help.

 

[emmanck123]

You're right, I have one more row. What I need help in is chosing which null row to use for obtaining the image. In the other exercises I have done, theres only one null row left and I use that one for my parameter for obtaining the image. In this case I have 2, my question is ¿how do I know which row to use?
Here's the finish row. I'll also add another exercise to show what I mean in regards to the image.