Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

7. Systems of Equations & Matrices

Introduction to Matrices

College Algebra

7. Systems of Equations & Matrices

Introduction to Matrices

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2:06 minutes

Problem 9

Textbook Question

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

Verified step by step guidance

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.

Square Matrices

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.

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). These types of matrices are essential in various applications, including vector representation and transformations, and they play a key role in understanding matrix operations.