Solve Systems of Linear Equations in MATLAB

Question

I have the following Equations

T2+T4-3.615*T1=0;
T1+10+2*T5-5.752*T2=0;
T1+38+2*T5-4*T4=0;
83+T4+T2+10-4*T5=0;

i've tried the following to find the values of T1,T2,T4,T5

syms T1 T3 T4 T2 T5 positive
T2+T4-3.615*T1=0;
T1+10+2*T5-5.752*T2=0;
T1+38+2*T5-4*T4=0;
83+T4+T2+10-4*T5=0;
sol=solve(T1,T2,T3,T4)

but its not working.

Answer 1

You have 4 equations and 4 unknowns. This is very easily solved in MATLAB using the equation AT = b, where T = A\b.

First move all the constant values over to the RHS. Then, reorder the equations to the form below (but don't write a11 = -3.615 etc in MATLAB, it's just to visualize it so that it's easier to create the A matrix below). If you have more equations and unknowns it might be easiest to do this with pen and paper before you create the matrix in MATLAB, as it's easy to get a sign wrong, or overlook a value somewhere.

a11*T1 + a12*T2 + a13*T3 + a14*T4 
a21*T1 + a22*T2 + a23*T3 + a24*T4
... and so on. 

Create a matrix A with the values a11, a12 ... all the way to a44. Now you can find the T's by using \ like this:

A = [-3.615  1       1    0;
     1      -5.752   0    2;
     1       0      -4    2;
     0       1       1   -4];
b = [0; -10; -38; -83];
T = A\b

T =  
   11.8878
   14.7558
   28.2188
   31.4936