Question

LU Decomposition Gauss Method EX4: Solve the same problem using the Gauss method. Example 4-6: MATLAB user-defined function for solving a system of equations using LU decomposition with Crout's method. ( Y Suggestions Use the code from the Crout's method. Discard the LUdecomp Crout module and leave the rest. Modify Gauss Pivot to store all the ratios Create the lower triangular matrix Confirm that L.U = A. Solve the problem by the LU double substitution Determine the currents ij, in, iz, and in in the circuit shown in the 392 figure (same as in Fig. 4-1). Write the system of equations that has to be solved in the form [a][i] = [b]. Solve the system by using the LU 24 V decomposition method, and use Crout's method for doing the decomposition. SOLUTION The currents are determined from the set of four equations, Eq. (4.1). The equations are derived by using Kirchhoff's law. In matrix form, [a][i] = [b], the equations are: 9 4 2 ol 4 17 -6 -3 12 - (4.44) -2 -6 14 -6 13 0 0 -3 -6 11 14 (18_ To solve the system of equations, three user-defined functions are created. The functions are as fol- lows: in 18 v

Answer 1

9 - -2 1 -6 á WO 12 Lai Loo o o 1 14 6 Laz o Ugu. ILI Luiz Lai L214 2+Lq2 L1 L310,2 +1.32 LIV L103 Lailly + L3224 Lailly + L 22 23 3 but h e Laruiz +232423 thaga Thal Luluiz + Lyz LG 3+ L42423 at Luz +4435 + Luh , L1=4 Luiz=-4 L31 = -2 Luo 222 = 137 solung LUX =3 0 LY-B od 3 boy 3739 1 = 17.8 i= 12.82 12. = 8.959 1. = 9.5