How Do You Write a Matrix?

According to Definition 2.3, a matrix appears as the coefficient 'A' in a specific type of mathematical expression known as a matrix equation.

Understanding the Matrix in a Matrix Equation

The provided reference, Definition 2.3, focuses on the structure of a matrix equation. It states that such an equation takes the form:

Ax = b

In this equation, the component representing the matrix is denoted by A.

• A is defined as an m×n matrix. This standard notation signifies the dimensions of the matrix.
  • The number 'm' represents the number of rows the matrix has.
  • The number 'n' represents the number of columns the matrix has.

The definition places the matrix 'A' directly before the vector x, indicating a matrix-vector multiplication. The result of this operation is the vector b.

While Definition 2.3 describes the matrix 'A' by its role in the equation and its dimensions (m×n), it highlights how a matrix functions within this foundational algebraic structure.

Equation Structure:
[Matrix] [Vector of Unknowns] = [Result Vector]
      A             x             =        b

In summary, when considering how a matrix is presented in the context of Definition 2.3, it is written as the coefficient 'A' in the matrix equation Ax=b, specified by its dimensions as an m×n matrix.