Circuit Theory/Thevenin-Norton

Vth using Node

 * $$V_{th} = 6.4516$$

In using Node

 * $$I_N = 1.064773736$$

Rth or Rn

 * $$V_{th}/I_N= \frac{6.4516}{1.064773736} = 6.0591 ohms$$

Finding Rth using source injection and node
Here is the mupad/matlab code that generates the answer Rth = 6.0591 ohms.

Comparing Node with Thevenin Equivalent
Solving the node equations yields:
 * $$V_a = 5.393$$
 * $$V_b = 1.1673$$
 * $$V_c = 1.107$$
 * $$i_{12} = 0.3571$$
 * $$v_{12} = 4.286$$

Using the Thevenin equivalent (and voltage divider) to compute voltage across the 12 ohm resistor:
 * $$v_{12} = V_s*\frac{12}{R{total}}$$
 * $$v_{12} = 6.4516*\frac{12}{6.0591+12} = 4.287$$

So they match ...

Thevenin voltage and resistance can not be computed from a node analysis of the entire circuit, but the node analysis of the entire circuit can be used to check if the thevenin equivalent produces the same numbers.