# Math Help - Matrix Street Traffic Problem

1. ## Matrix Street Traffic Problem

The question asks 'What is the solution vector for the unknown number of cars per day in this network of one-way streets?' I know that the number of cars going in equals the number going out, but I do not know how to approach setting up the matrix. I should be able to solve it from there on my own, but I just have no idea how to go about setting it up. Thank you.

2. For each of the four intersections, write down the equation which says that the number of cars entering the intersection per day is equal to the number of cars leaving the intersection. For example, the equation for the northeast corner (intersection of College and High) is $x_1+x_2 = N_2+N_3$.

The matrix form of these four equations should look like $\begin{bmatrix}1&1&0&0&N_2+N_3\\ 0&1&1&0&N_4+N_5\\ 0&0&1&1&N_6+N_7\\ 1&0&0&1&N_1+N_8\end{bmatrix}$. Now solve the equations by the usual process of reducing the matrix to diagonal form.

3. Thank you very much!