How to generate a system of four equations in four unknows to be solved in a matrix?

Create an m-file which generates the system of equations to be solved in matrix form and solves them using MATLAB. Comment your code so that it is clear what your vector of unknowns corresponds to in terms of vb and vc.

0=((v_b-v_a)./R_1)+((v_b-v_c)./R_5)+((v_b-v_d)./R_3)

0=((v_c-v_a)./R_2)+((v_c-v_b)./R_5)+((v_c-v_d)./R_4)

v_a=v_d+V_in

v_d=0

Assuming that V_in = 12 Volts, R_1=R_2=50W, R_3=R_4=100W, and R_5=1000W, create an mfile which generates the system of four equations in four unknowns to be solved in matrix form and solves them using MATLAB. Comment your code so that it is clear what your vector of unknowns corresponds to in terms of va , vb, vc and vd.

Answer 1

[John Doe]

If you are familiar with solving linear equations on matrix form by hand, you start of the same way:

A*x = b, where b = the voltages, and A is the matrix of (inverse) resistances. Then the solution in Matlab is simply

x = A\b

Better late than never... I believe this should solve your problem:

V_in = 12;
R = [50 50 100 100 1000];

A = [-1/R(1) 1/R(1)+1/R(5)+1/R(3) -1/R(5) -1/R(3);
    -1/R(2) -1/R(5) 1/R(2)+1/R(5)+1/R(4) -1/R(4);
    -1 0 0 1;
    0 0 0 1];

V = [0;0;-V_in;0];

x = A\V