Ubuntu doesn't recommend latest Nvidia drivers for installing CUDA 8

I want to install CUDA toolkit 8.0 on Ubuntu 16.04. My system has Nvidia GeForce 820M graphics card. CUDA 8 requires graphics drivers Nvidia-361 or higher.

System Settings > Software and Updates > Additional Drivers lists Nvidia-340 and Nouveau display driver to be the two options for drivers of graphics card. sudo ubuntu-drivers devices also recommends these two drivers, the following is the output:

== /sys/devices/pci0000:00/0000:00:1c.4/0000:08:00.0 ==
vendor   : NVIDIA Corporation
model    : GF117M [GeForce 610M/710M/810M/820M / GT 620M/625M/630M/720M] (GeForce 820M)
modalias : pci:v000010DEd00001140sv00001028sd00000652bc03sc02i00

driver   : nvidia-340 - distro non-free recommended
driver   : xserver-xorg-video-nouveau - distro free builtin

I however removed all the Nvidia graphics drivers using apt-get purge nvidia*, after which I installed the nvidia-361 using apt-get install nvidia-361. Now nvidia-smi lists following:

+------------------------------------------------------+                       
| NVIDIA-SMI 361.42     Driver Version: 361.42         |                       
|-------------------------------+----------------------+----------------------+
| GPU  Name        Persistence-M| Bus-Id        Disp.A | Volatile Uncorr. ECC |

| Fan  Temp  Perf  Pwr:Usage/Cap|         Memory-Usage | GPU-Util  Compute M. |
|===============================+======================+======================|
|   0  GeForce 820M        Off  | 0000:08:00.0     N/A |                  N/A |
| N/A   47C    P0    N/A /  N/A |    276MiB /  2047MiB |     N/A      Default |
+-------------------------------+----------------------+----------------------+

+-----------------------------------------------------------------------------+
| Processes:                                                       GPU Memory |
|  GPU       PID  Type  Process name                               Usage      |
|=============================================================================|

|    0                  Not Supported                                         |
+-----------------------------------------------------------------------------+

But the System Settings > Software and Updates > Additional Drivers still does not show Nvidia-361 to be the selected or recommended driver. Nouveau drivers are selected by default:

My concern now is that are nvidia-361 drivers compatible with my system and whether Ubuntu is using those or the Nouveau default drivers. Refer image below for Nvidia X Server Settings window: