Concept of Matrices and Calculations

Introduction

• Matrix: This is a rectangular arrangement of numbers, organized in rows and columns.
• Order: The order of the matrix is determined by the number of rows and columns. For example, 3x4 means 3 rows and 4 columns.

Matrix Addition

• Matrices can be added if their orders are the same.
• Example: To add two matrices C and D, add each of their corresponding elements.

Matrix Subtraction

• Just like addition, the orders need to be the same for subtraction as well.
• Subtract the corresponding elements.

Matrix Multiplication

• Important: Matrix multiplication is possible only when the number of columns in the first matrix is equal to the number of rows in the second matrix.
• Multiplication process: Multiply each element and take their sum.
• Example: A (3x2) and B (2x3)

  A = [a, b]
      [c, d]
      [e, f]
  B = [g, h, i]
      [j, k, l]
  
  Result = A.B
  

Determinant

• The scalar value of a square matrix
• Method to solve it: Special techniques for 2x2, 3x3 matrices.

Industry's Input-Output Model

• Definition: The internal and external use of products in different industries.
• Example: The production of the electricity industry and its usage in other industries.
• Matrix Transformation:
  • Producer and consumer-related calculations
  • General Input-Output Model: Ax = b
  • Unit Production Calculation: Based on the coefficient for each element.

Equilibrium Price and Total Value Addition

• Example:
  • Calculation of Gross Output: Determining the total production value
  • Total Value Addition: Considering payments to labor and other value-added factors

Conclusion

• All these concepts are about the fundamental usage of matrices and their calculations.
• Practice more and prepare for the quiz in the upcoming lecture.