The currents i₁, i₂, and i₃ in the circuit shown in Figure P12 are described by the following equation set if all the resistances are equal to R.

 

Here υ₁ and υ₂ are applied voltages; the other two currents can be found from i₄ = i₁ - i₂ and i₅ = i₂ - i₃.

a. Use both the matrix inverse method and the matrix division method to solve for the currents in terms of the resistance R and the voltages υ₁ and υ₂.

b. Find the numerical values for the currents if R = 1000 Ω, υ₁ = 100 V, and υ₂ = 25 V.

Figure P12