numerical methods question (please don't use matlab, and solve all of it by hand)

Q4) The following circuit has four resistors and two voltage sources. The resistors are R1, R2, R3 and R4 ohms; the voltage sources are E1 and E2 volts; and the currents are ij, iz and iz amps. i RI R2 DAWA R3 E2 WA R4 a. Using Kirchohoff's laws, derive the linear system for i, iz and iz. b. Using Gaussian elimination without pivoting, find ii, iz and iz when E1= 12 volts, E2= 10 volts, R1 = 2 ohms, R2 = 2 ohms, R3 = 4 ohms, and R4 = 1 ohm. C. If the resistances are changed to R1 = 0.001 ohms, R2 = 3.333 ohms, R3 = 4.002 ohms, and R4 = 0.012 ohms, find the currents ij, iz and iz using Gaussian elimination and 3-digit chopping arithmetic. d. Does partial pivoting improve the answer to part (c)? =