Find the dimension of each matrix. Identify any square, column, or row matrices. See the discussion preceding Example 1.
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Step 1: Understand the problem. We need to find the dimensions of each matrix and identify if they are square, column, or row matrices.
Step 2: Recall that the dimension of a matrix is given by the number of rows and columns it has, typically written as 'm x n', where 'm' is the number of rows and 'n' is the number of columns.
Step 3: A square matrix is one where the number of rows equals the number of columns (m = n).
Step 4: A column matrix is one that has only one column (n = 1), regardless of the number of rows.
Step 5: A row matrix is one that has only one row (m = 1), regardless of the number of columns.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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. Understanding dimensions is crucial for operations like addition, multiplication, and determining the type of matrix.
A square matrix is a matrix with the same number of rows and columns, meaning its dimensions are 'n x n'. Square matrices are significant in linear algebra because they can have properties like determinants and eigenvalues, which are not applicable to non-square 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). These types of matrices are essential in various applications, including vector representation and transformations, and they play a key role in understanding matrix operations.