I'm pretty new when it comes to working with Illustrator and Photoshop.
Basically I've got a vectorized Illustrator file at 2838 x 893 and I want to scale that as large as I can.
In Illutrator when I open it and select all objects and transform -> scale, the max it lets me is 200%. Then when I try to export as a JPG it tells me insufficient memory to complete the operation and when I try PNG it tells me the rasterized image is out of bounds.
So I tried saving as a PDF so I can rasterize the image in Photoshop, but the new PDF file is still at the original 2838 x 893 resolution.
Surely what I'm trying to do is possible and I'm missing a step somewhere?
You now have a fat huge monster Illustrator vector of more than 5 meters (almost 19').
Note: If you imported images that are raster and not vectors in your Illustrator, you cannot resize your artwork freely. Only vectors can be resized without any quality loss.
If you need to rasterize this and want it even bigger... Save that file and open that vector (.ai, .pdf, .eps) with Photoshop with the appropriate resolution. I think the max file dimension on opening is 270cm x 270cm (106.3" x 106.3") and the resolution you prefer. If you use pixels, you'll be limited at 32 000 pixels but you can get more by using the other units and a higher resolution.
Then you can go in the menu "image > image size" in Photoshop, uncheck the "resample" box and lower the resolution to what you need. If it's for web, you can lower it to 72ppi. The file dimension will increase as you lower the resolution. If you want more pixels, open your file at higher resolution.
You actually don't need to do the steps I mentioned in the first part if you plan is to use a JPG or PNG; doing the steps above simply help you getting an even bigger raster file in Photoshop. You can simply open your original vector in Photoshop with a very (crazy) high resolution and then lower the resolution to increase the image size as mentioned above.
Now, with that size, I don't think you can use the "save for web" to optimize you image but honestly, I don't see why you'd use this online anyway! You can still "save as" in jpg or png and stare at your spinning wheel while Photoshop saves your file. The maximum number of pixels in Photoshop is 300 000 x 300 000 pixels!
If you plan to use this for printing, you might as well simply stick to your vector file, it's a better quality. It's possible your computer won't let you create the biggest JPG in the world anyway and your printer can resize your vector without any issue. Simply create your file at a smaller size using a ratio (see this) and tell your printer what ratio you used.
If you're designing a billboard for example, you don't design it at its real size. You can design it 1/10 smaller and adjust your resolution accordingly (see links below). Ask your printer about it.