Grow light for in house plants with Arduino using LED

Thanks everyone I found some grow oriented Led strip that seems perfect for my purpouse.

I also already have a 12v - 3A power supply to drive it.

My question is now the following:
Can I have the whole system running with only one power supply?
will this circuit FRY my Arduino? I followed an example I found online and this is the circuit I currently have drafted but I can figgure out if it will blow it or not. Or even if it works XD.