You cannot invert the bx matrix so you should replace all

Question

You are given the four-bus problem as follows(Figure):

The data for this problem are as follows:
x12 = 0.2;
x14 = 0.4;
x13 = 0.25;
x24 = 0.5;
x34 = 0.1;

a. Form the 4 × 4 Bx matrix for this network. Use of Matlab is strongly recommended.
The first row will be
Bx = [(1/x12 + 1/x13 + 1/x14) - 1/x12 - 1/x13 - 1/x14]

b. You cannot invert the Bx matrix, so you should replace all elements in the fourth column by zeros, and replace all elements in the fourth row by zeros. Now replace the term Bx(4,4) by 1.0 and the matrix can be inverted. The result, which we shall call the X matrix, will be a 3 × 3 matrix corresponding to the first three rows and columns and the fourth row and column unchanged.

c. The generation and load on the system are

P_gen on bus 1 = 100.00 MW

P_gen on bus 2 = 150.00 MW

P_load on bus 3 = 350.00 MW

Assuming bus 4 as the reference, let theta for bus 4 be 0.0 radians. Assume S_base is 100 MVA.

d. You are going to solve a DC or linear power flow for this system. First convert all P_gen and P_load values to per unit, then solve for the bus phase angles on buses 1, 2, and 3. Then solve for the line flows on all transmission lines.