Back To Course

Algebra II Textbook26 chapters | 256 lessons

Are you a student or a teacher?

Try Study.com, risk-free

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Try it risk-freeWhat teachers are saying about Study.com

Already registered? Login here for access

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson to learn how easy it is to perform row operations on a matrix. Learn how to perform the three basic operations easily and quickly.

Matrices are everywhere in math. What is a **matrix**? It is an array of numbers arranged in rows and columns. Just think of numbers arranged nicely in a rectangular grid. Matrices come in all sizes. We call a matrix with 3 rows and 4 columns a 3 x 4 matrix. Yes, a matrix is defined by its size, the number of rows and columns, and when we give the size of the matrix, the rows always come first.

You will see these more and more often as you progress in your math career. Being able to perform operations on them will be very helpful to you. There are only three row operations: switching, multiplication, and adding. It is these three row operations that we will be looking at in this video lesson. I encourage you to come up with your own matrix and try out these three operations as we are talking about them.

The first row operation is **switching**. This operation is when you switch or swap the location of two rows. In this matrix, we can switch the first and third rows so that the 1 moves to the top.

The goal of switching is to get a better organized matrix. What I've done here is move the row with the leading 1 to the first row so that we have our first row beginning with a 1 and zeroes underneath the 1. Our matrix now begins with 1 in the first row, 0 in the second row, and 0 in the third row.

We can use arrows between our original matrix and the new matrix to show how we have switched the rows. For our matrix, we can put an arrow from the third row in the original matrix to the first row in the new matrix to show that we have switched the first row with the third.

Our next operation is **multiplication**. When we use this operation, we multiply one row with a certain number. The goal of multiplication is to get a better organized matrix. When we multiply one row by a certain number, we make sure we multiply each digit of our row with that number. For example, in this matrix, we can multiply the second equation by 1/5 to change the first non-zero number to a 1.

To show what you've done, you can write a little bit of notation between the beginning matrix and the end matrix. For what we have done, we can draw an arrow from the second row to the new second row and write (1/5)R sub 2 to show that we have multiplied the second row by 1/5.

The third and last operation is **addition**. This is when we add two rows together. The goal of adding two rows together is to simplify our matrix. We use addition when we can change a particular number to 0. For example, in this matrix, we can add the third row to the second row to change the first number in the second row to a 0.

To help us keep track of all of our changes, we note this operation by drawing an arrow from the beginning second row to the new second row and write on top of the arrow R sub 2 + R sub 3 so we know that we added row two to row three.

One thing to note here is that when we add two rows, we can choose which row to replace. If we are adding rows two and three, we can either replace row two or row three with the new row. We choose the one that will give us the simpler matrix.

We've covered all three operations separately. Let's combine them now. Yes, we can combine our operations to help us better organize and simplify our matrices. The most common combination is multiplying a certain row by a number and then adding it to another row to form a new row. For example, in this matrix, we can first multiply our first row by -2 and then add it to the third row so that the first number in the third row becomes 0.

To note this operation, we can draw an arrow from the beginning third row to the new third row and write on top of it -2R sub 1 + R sub 3 to tell us that we multiplied the first row by -2 and then added it to the third row. Notice because we are combining our operations, we left the first row the same even though we multiplied it by -2. This is perfectly okay.

Let's review what we've learned now. We've learned that a **matrix ** is an array of numbers arranged in rows and columns. A 3 x 2 matrix will have three rows and two columns. There are only three row operations that matrices have. The first is switching, which is swapping two rows. The second is multiplication, which is multiplying one row by a number. The third is addition, which is adding two rows together.

For each operation you do, it is recommended that you make note of what you did in between your matrices by drawing an arrow and writing little notes on top of the arrow. The goal of all these combined operations is to better organize and simplify your matrix.

You can also combine the operations to help you simplify your matrix. The most common combination is to multiply one row by a number and then add it to a different row.

Once you are done with this lesson you should be able to:

- Describe a matrix
- Modify a matrix through addition, multiplication, and switching, or a combination of the three
- Correctly notate the modification on the matrix

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackWhat teachers are saying about Study.com

Already registered? Login here for access

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
3 in chapter 10 of the course:

Back To Course

Algebra II Textbook26 chapters | 256 lessons

- What is a Matrix? 5:39
- How to Write an Augmented Matrix for a Linear System 4:21
- How to Perform Matrix Row Operations 5:08
- How to Solve Inverse Matrices 6:29
- How to Solve Linear Systems Using Gaussian Elimination 6:10
- How to Solve Linear Systems Using Gauss-Jordan Elimination 5:00
- Inconsistent and Dependent Systems: Using Gaussian Elimination 6:43
- Multiplicative Inverses of Matrices and Matrix Equations 4:31
- How to Take a Determinant of a Matrix 7:02
- Solving Systems of Linear Equations in Two Variables Using Determinants 4:54
- Solving Systems of Linear Equations in Three Variables Using Determinants 7:41
- Using Cramer's Rule with Inconsistent and Dependent Systems 4:05
- How to Evaluate Higher-Order Determinants in Algebra 7:59
- Go to Algebra II: Matrices and Determinants

- Introduction to HTML & CSS
- Introduction to JavaScript
- Computer Science 332: Cybersecurity Policies and Management
- Introduction to SQL
- Computer Science 203: Defensive Security
- JavaScript Language Basics
- Error Handling, Debugging & Events in JavaScript
- HTML Elements & Lists
- Conditionals, Arrays & Loops in JavaScript
- Introduction to HTML
- Anti-Bullying Survey Finds Teachers Lack the Support They Need
- What is the ASCP Exam?
- ASCPI vs ASCP
- MEGA Exam Registration Information
- MEGA & MoGEA Prep Product Comparison
- PERT Prep Product Comparison
- MTLE Prep Product Comparison

- Simple Scientific Tools & Uses for Kids
- Chi Square Distribution: Definition & Examples
- Stars: Definition & Facts
- Linear Approximations Using Differentials: Definition & Examples
- Access Control: Types & Implementation
- 'I Am' Poem Lesson Plan
- Key Controls in Cybersecurity Risk Management: Definition & Use
- Quiz & Worksheet - Line Integrals
- Quiz & Worksheet - Frankenstein Creature Quotes
- Quiz & Worksheet - A Christmas Carol Facts
- Quiz & Worksheet - Preschool Classroom Technology
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies
- Free Lesson Plans
- ESL Games

- Earth Science for Teachers: Professional Development
- Ohio Graduation Test: Study Guide & Practice
- Introduction to Financial Accounting: Certificate Program
- Calculus for Teachers: Professional Development
- Abnormal Psychology: Certificate Program
- CEOE Physical Science: Thermodynamics
- Method & Composition: MTLE Middle Level Communication Arts/Literature
- Quiz & Worksheet - Angular Momentum
- Quiz & Worksheet - Types of Reactions to Stress
- Quiz & Worksheet - James-Lange & Cannon-Bard Theories of Emotion
- Quiz & Worksheet - Crowding Out in Economics

- Organizational Climate: Definition, Factors & Impacts on Culture
- Organism Tolerance for Atmospheric Conditions
- How Long is the TABE Test?
- Scoring Changes on the New SAT
- How to Write a Good College Essay
- Ancient History Documentaries
- Logic Games for Kids
- Logic Games for Kids
- AP English Literature Question Types
- Kindergarten Writing Prompts
- Independent Study Programs
- Free LSAT Practice Test

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject