Linear algebra may sound like a complex term, but when you break it down, its all about relationships between two or more entities. For person involved in economics, its a powerful tool that can help you solve and analyze various problem in the field of economy. Either it be Microeconomics, or Macroeconomics.
Before understanding the uses of linear algebra in economics, let me explain you what linear algebra actually is. Linear algebra is a study of matrices, vectors and linear transformation. Matrices and vector are used to represent the data in a structured way, and linear transformation is a function to transform the data in a meaningful way.
In economics, we often have to use data, equations and models to solve a specific problem. Those data can be represented using linear algebra using matrices and vectors.
Vector is a one dimensional array of values. In economics, vectors can be used to represent quantity of goods, prices or items. Imagine you have two items apples and bananas in your inventory. You can use vector to represent the quantity of apples and bananas you have using vector.
\(V = \begin{bmatrix}
10 \\
20
\end{bmatrix}
\)
Here, 'V' is a vector representing the quantity of apples and bananas you have. The first value 10 represents the quantity of apples and the second value 20 represents the quantity of bananas.
Matrices are special structure that can be used to represent data as well as act on it. Matrix is special because of its different properties like inverse, matrix multiplication, determinants and so on.
In economics, matrices can be used to represent economic models. For example, consider a simple economic model, where you have two variables, price and quantity. You can represent this model using matrix as follows:
\(A = \begin{bmatrix}
2 & 3 \\
4 & 5
\end{bmatrix}
\)
where first column represents the price and second column represents the quantity.
Linear algebra provides powerful data structures (matrices) and operations (linear transformations) that can be used to represent related data like (price , quantity of goods) in a structured way.
So when they want to perform operation like finding the unknown quantity, or finding the optimal price, or break even values, they can use equations and models of linear algebra to solve the problem.