Skill: Determine the dimensions of a matrix

Explanation and Free Practice Resources

A matrix’s dimensions, or order, are given as rows × columns: the first number counts horizontal rows and the second counts vertical columns. This describes the matrix’s rectangular structure, not the values of its entries; an m×nm \times n matrix has mm rows and nn columns, and is square when those counts are equal. The description applies to finite matrices, not infinite arrays or abstract vector-space dimensions.

Detailed Explanation: Determine the dimensions of a matrix

To find a matrix’s dimensions, count its rows first (horizontal lines of entries), then its columns (vertical lines of entries). Write the result as rows ×\times columns.

For example, consider

A=[2−14035].A=\begin{bmatrix} 2 & -1 & 4\\ 0 & 3 & 5 \end{bmatrix}.
  1. Count the horizontal rows: there are 22.
  2. Count the vertical columns: there are 33.
  3. Write rows ×\times columns: AA is a 2×32\times 3 matrix.

The dimensions describe the matrix’s rectangular shape, not the values of its entries. Since 2≠32\ne 3, this matrix is not square.

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Matrices - Identify Dimensions


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