I tried to use node-voltage/ linear algebra but I am getting some strange values
Here is the question and my work:

http://imgur.com/a/h7uoU

thanks!

 

I would try converting the voltage source to a current source. Then simplify the circuit and repeat. This should simplify down to Thevenin and Norton equivalent circuits. Max power is deliver to the load when the source (or everything before a and b terminals) is equal to the load. I don't know what the second question is on about

At least thats what I think...

 

I found out the way I did the first part was correct. The problem seems to be my linear algebra. I tried to use the rref() function on my calculator but it was giving me those strange values I wrote on my paper. I ended up using wolfram alpha to solve the matrix and got values that looked more realistic.