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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1:42 minutes

Problem 1

Textbook Question

How many rows and how many columns does this matrix have? What is its dimension? <4x2 Matrix>

Verified step by step guidance

Step 1: Understand that a matrix is defined by its rows and columns.

Step 2: Identify the number of rows in the matrix. In a matrix, rows are the horizontal lines of elements.

Step 3: Identify the number of columns in the matrix. Columns are the vertical lines of elements.

Step 4: The dimension of a matrix is given in the form 'rows x columns'.

Step 5: For a 4x2 matrix, it has 4 rows and 2 columns, so its dimension is 4x2.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Matrix

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. Each element in a matrix is identified by its position, defined by its row and column indices. Matrices are fundamental in various fields, including algebra, statistics, and computer science, as they can represent systems of equations, transformations, and more.

Rows and Columns

In a matrix, rows are the horizontal lines of elements, while columns are the vertical lines. The number of rows indicates how many horizontal groupings of elements exist, and the number of columns indicates how many vertical groupings there are. Understanding the arrangement of rows and columns is essential for determining the structure and properties of the matrix.

Matrix Dimension

The dimension of a matrix is expressed as 'm x n', where 'm' represents the number of rows and 'n' represents the number of columns. This notation provides a concise way to describe the size of the matrix. For example, a 4x2 matrix has 4 rows and 2 columns, indicating its structure and the number of elements it contains.