Application of linear systems - Linear Equations with Matrices

Notes:

We will be looking at real-life problems involving linear algebra. The three types of real-life applications we will be looking at are:

1. Linear systems in Economics

2. Linear systems with Chemical Equations

3. Linear systems with Network Flow

In economics, we can use linear algebra to determine the equilibrium price of outputs for each sector. Note that in order to get the equilibrium price, we need to set

Income = expenses (expenditures)
In Chemistry, we can use linear algebra to balance chemical equations like: $N_2+H_2$→$NH_3$
We do so by counting the number of elements in a compound, and turning each coefficient as a variable to solve.

We can also use linear algebra to study the flow of some quantity through a network. Make sure that for each node: Flow in = Flow out
Our goal is to make all of these questions into matrix, and then solve.