Solving Op amp with nodal equations

[Alex Santos]

Homework Statement

Find V0 and i0 of the circuit.

Homework Equations

KCL

The Attempt at a Solution

I tried multiple times and never got the right answer.
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Hello, I am having trouble solving a problem. I will link a picture of the problem with answers, but it just seems I can't get it right. Also if someone has a good rule of thumb when applying direction of current it would be highly appreciated to get to know it.

 

[gneill]

Can you show us at least one of your attempts? It's a Forum requirement that before you can receive help you must show some attempt in order that helpers can evaluate the level of help you need.

 

[Jony130]

Pleas show as your attempt. And do you know that if op amp works in linear region the voltage at inverting input will be 0V.

 

[Alex Santos]

Yes of course I am trying to do this once again, I will post my results and show you.

 

[Alex Santos]

Here is my attempted result, as you can see the current I₀ is incorrect and therefor the rest of the problem is incorrect. Any tips on strategy how to solve those problems is welcome.
Thank you for taking the time to help me.

 

[Alex Santos]

Here is another attempt, This time I got the current right but in the wrong direction, It confuses me how to determine the direction of current, It always seems like its flowing out of the node all the time at every node.

 

[gneill]

I don't see where you determined V3 to plug into the last equation. Otherwise you seem to be doing okay.

 

[NascentOxygen]

It's an inverting amplifier, so V3 is going to be -6V here.