The dimensions of a matrix can be determined by counting the number of rows and columns it has. Any matrix can be represented as m x n, where m denotes the number of rows, and n denotes the number of columns.

  To determine the dimensions of a given matrix, you can follow these steps:

  1. Count the number of rows: Start from the top of the matrix and count the number of horizontal lines. Each line represents a row, so the number of horizontal lines is the number of rows in the matrix.

  2. Count the number of columns: Look at any row within the matrix and count the number of vertical lines. Each vertical line represents a column, so the number of vertical lines in any row gives you the number of columns in the matrix.

  3. Express the dimensions as m x n: Once you have determined the number of rows and columns, write the dimensions of the matrix as m x n.

  For example, let's consider the matrix below:

  1 2 3

  4 5 6

  To determine the dimensions of this matrix:

  1. Count the number of rows: There are two horizontal lines, so there are 2 rows.

  2. Count the number of columns: The first row has 3 vertical lines, so there are 3 columns.

  3. Express the dimensions: Therefore, the dimensions of the matrix are 2 x 3.

  In summary, the dimensions of any matrix can be determined by counting the number of rows and columns it has.