How do you solve this circuit using mesh and nodal analysis?

Mesh analysis:

There are 4 meshes in this circuit. Each mesh namely I1, I2, I3, I4 are the currents in the corresponding mesh. The mesh equations of the system are based on KVL (Kirchoff’s Voltage Law) that voltages around the mesh sums up to 0 (zero). Organize the equation will lead to the R matrix:

R’s in I1 | -mutual R between I1 and I2 | -mutual R between I1 and I3 | -mutual R between I1 and I4 |

-mutual R between I1 and I2 | R’s in I2 | -mutual R between I2 and I3 | -mutual R between I2 and I4 |

-mutual R between I1 and I3 | -mutual R between I2 and I3 | +R’s in I3 | -mutual R between I3 and I4 |

-mutual R between I1 and I4 | -mutual R between I2 and I4 | -mutual R between I3 and I4 | R’s in I4 |

You can visually identify the correctness of this matrix and then solve for it based on

V=RI matrices and get

I=inv(R)xV

Here is the matrix R:

You can do the same for nodal analysis except to convert the voltage sources to current sources using ohm’s law:

IA=V1/R1 and IC=V2/R6 where IA is current going to node A and IC is current going to node C.

Now you can set up the nodal equation similar to that of the mesh equation except now for VA, VB and VC, only 3×3 matrix.

V=RI matrices becomes I=GV

and to solve for V=inv(G)xI

G’s connected to VA | -mutual G between VA and VB | -mutual G between VA and VC |

-mutual G between VA and VB | G’s connected to VB | -mutual G between VB and VC |

-mutual G between VA and VC | -mutual G between VB and VC | +G’s connected to VC |