Find the dimension of each matrix. Identify any square, column, or row matrices. See the discussion preceding Example 1. <5x1 Matrix>

Verified step by step guidance

1. Step 1: Understand the notation of a matrix. A matrix is typically represented as a rectangular array of numbers arranged in rows and columns.
2. Step 2: Identify the dimensions of the matrix. The dimensions of a matrix are given in the form 'm x n', where 'm' is the number of rows and 'n' is the number of columns.
3. Step 3: Analyze the given matrix notation '<5x1 Matrix>'. This indicates that the matrix has 5 rows and 1 column.
4. Step 4: Determine the type of matrix. A matrix with only one column is known as a column matrix.
5. Step 5: Check if the matrix is a square matrix. A square matrix has the same number of rows and columns. Since this matrix has 5 rows and 1 column, it is not a square matrix.

Key Concepts

Matrix Dimensions

The dimension of a matrix refers to its size, expressed in terms of rows and columns. It is denoted as 'm x n', where 'm' is the number of rows and 'n' is the number of columns. For example, a 5x1 matrix has 5 rows and 1 column, indicating it is a column matrix.

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 3x3 matrix is square because it has three rows and three columns. Square matrices are significant in linear algebra as they can have properties like determinants and eigenvalues.

Row and Column Matrices

A row matrix is a matrix with a single row, while a column matrix has a single column. For example, a 1x5 matrix is a row matrix, and a 5x1 matrix is a column matrix. These types of matrices are often used in vector representation and can simplify operations in linear algebra.