Ch 22: MTEL Middle School Math/Science: Matrices in Linear Algebra

About This Chapter

In your preparations for the MTEL: Mathematics/Science (Middle School) exam use this chapter to review the functions of the matrix form of linear systems and the operations you can perform with them.

MTEL Middle School Math/Science: Matrices in Linear Algebra - Chapter Summary

Prior to taking the exam, use these lesson videos to review the steps used to write systems of equations in a matrix form. You may also explore the different operations you can complete within the matrix. Each lesson is taught by an expert instructor who will walk you through example problems and explain:

  • How to write linear systems in matrix form
  • Performing matrix operations and determining if two matrices are alike
  • Completing matrix row operations
  • Uses and operations for finding inverse matrices
  • Gaussian elimination and solving linear systems
  • Purpose of Cramer's Rule with inconsistent and dependent systems
  • Finding the determinant of a matrix

After completing a lesson, take the quiz that accompanies it to test your retention of the material. Once you get your quiz results, review them so that you can improve your understanding of the above concepts. If you find any topics that you are unable to master, use the teacher tab of the lessons to get assistance from our instructors.

MTEL Middle School Math/Science: Matrices in Linear Algebra Objectives

The Massachusetts Tests for Educator Licensure (MTEL): Mathematics/Science (Middle School) exam is a four-hour exam used to measure the mathematical and scientific competencies of future middle-grades math and science teachers in the state of Massachusetts. To complete its objective, this computer-based exam asks test takers to complete 100 multiple-choice questions and two open-response assignments. Of the material that your score will be based on, 5% is about trigonometry, calculus and discrete mathematics. This chapter will help you prepare for some of these questions by improving your understanding of matrices the operations of matrices.

9 Lessons in Chapter 22: MTEL Middle School Math/Science: Matrices in Linear Algebra
Test your knowledge with a 30-question chapter practice test
What is a Matrix?

1. What is a Matrix?

As math gets more and more complicated and there become more and more numbers flying around, it becomes really handy to put all these numbers in a nice organized grid... hello matrices! Learn about what they are and why there are used.

How to Write an Augmented Matrix for a Linear System

2. How to Write an Augmented Matrix for a Linear System

Watch this video lesson to learn how you can turn your system of equations into matrix form. The matrix form is another way of writing your linear system that is sometimes easier to work with.

Matrix Notation, Equal Matrices & Math Operations with Matrices

3. Matrix Notation, Equal Matrices & Math Operations with Matrices

Watch this video lesson to learn about the basics of matrices and what kinds of math operations you can do with them. Also learn how to determine whether two matrices are the same or not.

How to Perform Matrix Row Operations

4. How to Perform Matrix Row Operations

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.

How to Solve Inverse Matrices

5. How to Solve Inverse Matrices

Watch this video lesson to learn what kinds of matrix operations you can take to find the inverse of a matrix. Also learn why matrix inverses are useful.

Multiplicative Inverses of Matrices and Matrix Equations

6. Multiplicative Inverses of Matrices and Matrix Equations

Watch this video lesson to learn about another method you can use to solve a matrix problem if you are given the inverse of the matrix. You will also learn the identifying mark of the multiplicative inverse of a matrix.

How to Solve Linear Systems Using Gaussian Elimination

7. How to Solve Linear Systems Using Gaussian Elimination

Watch this video lesson to learn an easy way to solve a system of equations that involves manipulating a matrix. Learn the kinds of easy matrix manipulations that are needed to solve any system of equations.

Using Cramer's Rule with Inconsistent and Dependent Systems

8. Using Cramer's Rule with Inconsistent and Dependent Systems

Watch this video lesson, and you will see what happens when we use Cramer's Rule with inconsistent and dependent systems. You will see what kind of result you will always get when you try to use Cramer's Rule.

How to Take a Determinant of a Matrix

9. How to Take a Determinant of a Matrix

Matrices are incredibly powerful and can help you do all sorts of things, but one of the most basic (and surprisingly helpful) operations you can perform on one is to take its determinant. Learn how to do that here!

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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Other Chapters

Other chapters within the MTEL Mathematics/Science (Middle School)(51): Practice & Study Guide course

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