So my book asks me to find \$i_a, i_b, i_c\$ (as functions of \$v_1, v_2, v_3\$) as well as \$G_a, G_b, G_c\$ such that the circuit on the right picture (shown below) is equivalent to the circuit on the left. First he suggests to use Y-Δ transform to find \$G_a, G_b, G_c\$ with equivalent resitances \$R_1, R_2, R_3\$.
As you can see I duplicated each current source adding a short circuit (which it can be shown not to invalidate Kirchhoff's laws, thus obtaining parallel of the current source and resistance, which ultimately can be transformed to a voltage source). However, the resulting linear system has 0 determinant: what is wrong with my reasoning? How would you solve this exercise?