What's Inside this Chapter?
What’s Inside the Chapter? (After Subscription)
1. Introduction to Matrices
1.1. Types of Matrices
2. Matrix Operations
2.1. Addition and Subtraction
2.2. Scalar Multiplication
2.3. Matrix Multiplication
2.4. Transpose of a Matrix
3. Determinants
4. Inverse of a Matrix
5. Rank of a Matrix
6. Systems of Linear Equations and Cramer’s Rule
7. Eigenvalues and Eigenvectors
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Determinants Matrix
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Mathematical Methods in Economics
Introduction to Matrices
A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns, and it forms one of the most fundamental tools used in economic analysis, particularly in input-output analysis, econometrics, and optimization theory. A matrix of order \(m \times n\) has (m) rows and (n) columns, and is generally written as:
$$
A =
\begin{bmatrix}
a_{11} & a_{12} & \cdots & a_{1n} \\
a_{21} & a_{22} & \cdots & a_{2n} \\
\vdots & \vdots & \ddots & \vdots \\
a_{m1} & a_{m2} & \cdots & a_{mn}
\end{bmatrix}
$$
Each element \(a_{ij}\) refers to the entry located in the (i)-th row and (j)-th column. The order or dimension of a matrix is expressed as (rows × columns). Matrices are central to representing systems of linear equations, transformations, and economic models involving multiple variables such as the Leontief input-output model.