What is the equivalent resistor seen from two terminals on the left?

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The discussion revolves around finding the equivalent resistor seen from two terminals in a circuit with R1 at 1K Ohm and R2 at 50K Ohm, alongside a transconductance of 100mA/V. The user attempted to apply a test voltage source but encountered difficulties due to having two variables in the equivalent resistor equation. They expressed a need for assistance, particularly in demonstrating their approach and equations used. Other participants encouraged sharing specific attempts to facilitate better guidance. The conversation highlights the challenges of circuit analysis and the importance of collaboration in problem-solving.
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Homework Statement


R1 = 1K Ohm
R2= 50K Ohm
gM = 100mA/V

I should find the equivelent resistor seen from the two terminals on the left


Homework Equations



Nodes equations, Ohm's law.

The Attempt at a Solution



So, I started by putting a test voltage source on the left but I end up with 2 variables on the equivalent resistor equation that I can't be able to solve.
I did Circuit analysis last year, which I passed but now I'm a bit rusty with this. Anyone can help me?
 

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Can you show what you've tried? Show your equations.
 

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