Creating and solving large systems of equations I am trying to follow a solution in a book so that I can build my own model. They produce the set of equations below. The book claims it to be a system of equations with 10 unknowns; however from my understanding, to solve a system of equations, each equation in the system must have all of the unknowns for the solver to work. So I am wondering whether I have to rearrange all the equations so that each unknown appears in every equation? This seems like a very long process and I will definitely make an error somewhere. Is there an alternative to doing this or is this the only way? Thanks for any help you can offer.     

All of the variables do appear in each linear equation, but some of them have coefficient zero. For example, we could write the first equation as
$$
T_0 - 2T_1 + T_2 + 0T_3 + 0T_4 + 0T_5 + 0T_6 + 0T_7 + 0T_8 + 0T_9 + 0T_{10}.
$$
When you write out the matrix that corresponds to this system of linear equations it will have many zeroes. I don't expect that the problem is easy to solve, but you should not have any trouble setting it up from a linear algebra perspective.
