circuit analysis
Using Multisim, I was able to calculate these current values, however I can't seem to understand their correlation with the individual mesh loop current values I calculated using matrices in MATLAB.
In my calculations, i1 is 3A, i2 is 2A, and i3 is 4A. How would I show that the data in this model supports these calculations?
The node voltage equations are not so difficult. But it's really a tedious work to type the equations. I got the same result with you, maybe we are both wrong :).
Using the mesh or node equations, you should be able to determine each of the currents and voltages in the circuit in terms of \$V_{in}\$ and \$I_{in}\$. This will give you 10 equations of the form
$$V_j = f_j\left(V_{in},I_{in}\right)$$ and $$I_k = g_k\left(V_{in},I_{in}\right)$$
Now you say you are given the power consumed by each resistor, which means a set of equations of the form
$$V_nI_n=P_n$$
where the \$P_n\$ are known values.
This will be more than enough equations to be able to determine \$V_{in}\$ and \$I_{in}\$. All you need to do is pick the most convenient couple of equations and do some algebra.
Best Answer
Your mesh currents are wrong. These are the correct equations:
$$\begin{align} I_1R_1+(I_1-I_3)R_3+(I_1-I_2)R_2&=0\\ (I_2-I_1)R_2+(I_2-I_3)R_4&=15V\\ (I_3-I_2)R_4+(I_3-I_1)R_3&=21V \end{align}$$
Solving this system gives the following mesh currents:
$$\begin{align} I_1&=18.000\,A\\ I_2&=21.545\,A\\ I_3&=20.818\,A \end{align}$$
All currents in the network can be calculated from these mesh currents, and the results correspond to the ones obtained by Multisim, e.g. the current through \$R_2\$ is \$I_2-I_1=3.5455\,A\$.