Find the dimension of each matrix. Identify any square, column, or row matrices. See the discussion preceding Example 1. <1x2 Matrix>

Verified step by step guidance

1. Step 1: Understand the concept of matrix dimensions.
2. Step 2: Identify the number of rows and columns in the given matrix.
3. Step 3: Recognize the format of the matrix as 1x2, meaning 1 row and 2 columns.
4. Step 4: Determine if the matrix is a square matrix. A square matrix has the same number of rows and columns.
5. Step 5: Identify the matrix as a row matrix because it has only one row.

Key Concepts

Matrix Dimensions

The dimension of a matrix is defined by its number of rows and columns, typically expressed as 'm x n', where 'm' is the number of rows and 'n' is the number of columns. For example, a matrix with 1 row and 2 columns is referred to as a 1x2 matrix. Understanding dimensions is crucial for operations like addition, multiplication, and determining compatibility between matrices.

Square Matrices

A square matrix is a matrix that has the same number of rows and columns, denoted as 'n x n'. For instance, a 2x2 matrix is square because it has 2 rows and 2 columns. Square matrices are significant in linear algebra as they are involved in operations such as finding determinants and inverses, which are not applicable to non-square matrices.

Row and Column Matrices

A row matrix is a matrix with a single row (1 x n), while a column matrix has a single column (m x 1). For example, a 1x2 matrix is a row matrix, and a 2x1 matrix is a column matrix. These types of matrices are important in various applications, including vector representation and transformations in linear algebra.