Question 2.14: Write the mesh equations directly in matrix form for the cir...

The matrix equation is:

Notice that mesh 1 includes R_2, R_4 , and R_5, so the r_{11} element of R is the sum of these resistances. Similarly, mesh 2 contains R_1, R_2, and R_3, so r_{22} is the sum of these resistances. Because R_2 is common to meshes 1 and 2, we have r_{12} = r_{21} = −R_2.
Similar observations can be made for the other elements of R.

As we go around mesh 1 clockwise, we encounter the positive reference for v_A first and the negative reference for v_B first, so we have v_1 = −v_A + v_B, and so forth.