Does the Raspberry Pi Zero v1.3 support TensorFlow? I came across online that the ArmV7 used in above Pi board do not have right instructions to handle the above framework? Is it true?
I assume you're referring to this GitHub issue, in which the following is stated:
It looks like Pi Zero isn't going to work for TensorFlow, unfortunately. ARMv6 just doesn't have the right instructions to be able to handle the software
There's no reason to disbelieve the maintainer here, and it does indeed seem that no-one else has managed it since (at least not visible despite copious searching).
The closest I'm aware of is Google's AIY Projects Vision Kit, which runs a TensorFlow network on a co-processor connected to the Pi Zero W in this kit. The co-processor is an Intel Movidius VPU and the kit is apparently for sale for $45. It's worth noting the co-processor is specifically designed for vision applications using convnets and I'm unsure if it even supports anything other than the video input from the camera.
You also are expected to train the network on a more powerful computer; doing so on the Pi, even with the co-processor, would be pointless and would waste your time. Training a neural network is pretty intensive, and the Pi Zero simply would not be up to it in reasonable times.