Circuit Analysis Help

I'm having trouble figuring out the analysis of the first circuit located at this link:

https://www.ece.ucsb.edu/Faculty/rodwell/Classes/ECE137A/more_opamp_hints.pdf

It claims that the open loop gain can be found to be 101Vout/Vx (where Vx is the node beween the two 10 khm: resistors)

i don't understand how they came to this conclusion. Seeing as how the 1 khm: resistor is connected to ground and a virtual ground, how is it relevant to the analysis? also, the 100khm: resistor should (ideally) not have current running through it. could somebody show me the mathematical analysis of this circuit?