How To Root the Galaxy Tab 10.1v

As always, mucking with your device at this level is risky. If you follow this process, you do so entirely at your own risk. I accept no responsibility for any detrimental effects resulting from following this process of rooting the galaxy tab, or for any problems associated with the updated files. Only if you accept these risks should you use these instructions.
NOTES:
I developed and followed this process on Ubuntu Natty, 64bit. I see no reason why it should not work on any other platform, since the only tool used is fastboot and the syntax for fastboot is the same on any platform. if you need to know how to get fastboot working, there are already many guides for that (see my how to unlock your bootloader thread, for example)
BUTTON CONFUSION:
When in landscape mode, with the camera at the top, the power button is on the left ‘vertical’ side of the tab. On the top is the volume rocker. In this orientation:
- The LEFT side of the volume rocker is VOLUME DOWN
- The RIGHT side of the volume rocker is VOLUME UP
This might seem obvious, but to anyone who is used to phones, this is the opposite, since they were designed to be used in Portrait mode.
PREPARE:
1) With your Tab in fastboot mode (step 1 of “GETTING ROOT” below), make sure you have a working fastboot implementation:
[CODE]fastboot devices[/CODE]
If all is well, you should see your device serial number. If there is a problem, you won’t get any response.
2) Downlad the two files attached to this thread
3) Create a folder on your desktop called “root”
[CODE]mkdir ~/Desktop/root[/CODE]
for Ubuntu or
[CODE]md %userprofile%\desktop\root[/CODE]
for Windows
This will be referred to as the working directory throughout the rest of this guide
4) Copy skitzandroid-10-1v-root.zip to your working directory (DO NOT UNZIP!)
5) Extract the skitzandroid-recovery.img file from skitzandroid-stock-recovery.zip to your working folder. Your working folder should now have 1 IMG file and one ZIP file.
6) This was an afterthought – Make sure fastboot is somewhere in your path (ie can be executed from anywhere). To test, ‘cd’ to any random folder and type ‘fastboot’ and make sure it runs.
7) Copy the skitzandroid-10-1v-root.zip file to the root of your sdcard. You can eithe drag/drop, or run:
[CODE]adb push skitzandroid-10-1v-root.zip /sdcard[/CODE]
from your working directory
…now the easy part
GETTING ROOT:
1) Power off your Tab and power it back on, while holding the VOLUME DOWN button.
2) When the DOWNLOAD / FASTBOOT icons appear, press VOLUME DOWN again to select FASTBOOT icon (the one with the USB logo) and press VOLUME UP to confirm selection.
3) Confirm you are now in fastboot mode and do a:
[CODE]fastboot devices[/CODE]
If all is well, you should see your device serial number.
4) Open a terminal / CMD prompt and CD to your working folder
[CODE]cd ~/Desktop/root[/CODE]
for Ubuntu or
[CODE]cd %userprofile%\desktop\root[/CODE]
for Windows
5) Run the following command:
[CODE]fastboot boot skitzandroid-recovery.img[/CODE]
..and wait. It might not look like anything is happening but it is.
6) You should now have a recovery menu. Use the volume rocker (up/down navigates menu options) to select “Install zip from SDCARD” (or something like that – if someone can post the exact menu item wording, I will update the guide). Press (tap!) the POWER button to confirm the menu selection
7) Navigate to the root of your internal storage (/sdcard), select the skitzandroid-10-1v-root.zip file and press (tap!) the POWER button to confirm selection.
 Once complete, use the Volume rocker to select “REBOOT” from the menu and press (tap!!!) the POWER button to confirm selection.
9) YOUR’RE DONE. Press the thanks button on this thread to continue 
TESTING:
1) Check your apps menu to confirm the existence of SuperUser app.
2) With the Tab attached to your PC via USB cable, do the following:
[CODE]adb shell
su[/CODE]
And watch the screen on your Tab for a SuperUser prompt. If you see this, congratulations!
If you have never rooted a phone/tablet before, go get Titanium Backup Pro and ROM Manager from the market. As soon as the custom ROMs start flowing in, you’ll be all set to go.
Source.