# Ch 25: MTEL Math: Vectors, Matrices & Determinants

### About This Chapter

## MTEL Math: Vectors, Matrices & Determinants - Chapter Summary

The goal of the lessons in this chapter is to refresh your knowledge on matrices, vectors and determinants. Learning about these math topics will get you fully prepared for the exam. You will also be able to review:

- The dot product of vectors
- Definition of a matrix
- Writing augmented matrices for linear systems
- Matrix row of operations
- Solving inverse matrices
- Using Gaussian elimination to solve linear systems
- Taking a determinant of a matrix
- Evaluating higher-order determinants

We have put together the perfect resources to help you study efficiently for the MTEL Math exam. Since our materials feature a video format, and you can get help from online instructors, picking up strategies that will help you work with vectors and matrices is easy.

### MTEL Math: Vectors, Matrices & Determinants Chapter Objectives

If you are seeking a license to teach math in Massachusetts, you will need to pass the MTEL Math exam. It contains different sections, and the topics in this chapter are included on subarea 2. This part makes up 23% of the exam and contains multiple-choice questions and possibly open-response questions.

Review our video lessons to quickly pick up info about different math topics like matrices and determinants of matrices. Once you have finished looking through every lesson, go ahead and test your knowledge using our self-assessment quizzes. They are brief and effective at helping you decide if you are ready for the exam.

### 1. Performing Operations on Vectors in the Plane

After watching this video lesson, you should be able to add, subtract, and multiply your vectors. Learn how easy it is to perform these operations and what you need to keep in mind when performing these operations.

### 2. The Dot Product of Vectors: Definition & Application

After watching this video lesson, you will be able to find the dot product of vectors both algebraically and geometrically. Learn the difference between the two and what you need in order to calculate them.

### 3. 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.

### 4. 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.

### 5. 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.

### 6. 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.

### 7. 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.

### 8. 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.

### 9. Inconsistent and Dependent Systems: Using Gaussian Elimination

Watch this video lesson to learn whether or not you can use Gaussian elimination to solve inconsistent and dependent systems. Also, learn whether there is another way to find solutions of these systems.

### 10. 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.

### 11. 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!

### 12. Solving Systems of Linear Equations in Two Variables Using Determinants

Watch this video lesson to learn how you can easily find the solution of a linear system in two variables by just using determinants. All you need to find the complete solution is to find three determinants.

### 13. Solving Systems of Linear Equations in Three Variables Using Determinants

Watch this video lesson to learn how to use Cramer's rule to help you find your solutions by finding just four determinants. Learn the numbers to use for your determinants.

### 14. How to Evaluate Higher-Order Determinants in Algebra

Watch this video lesson to learn the rules for taking the determinant of any size matrix. Learn the kind of matrix that you need before you can take the determinant. Watch as the pattern of the determinant takes shape.

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### Other Chapters

Other chapters within the MTEL Mathematics (09): Practice & Study Guide course

- MTEL Math: Basic Arithmetic Operations
- MTEL Math: Absolute Value & Integers
- MTEL Math: Fractions
- MTEL Math: Decimals
- MTEL Math: Percents
- MTEL Math: Rates & Ratios
- MTEL Math: Proportions
- MTEL Math: Estimation
- MTEL Math: Origins of Math
- MTEL Math: Rational & Irrational Numbers
- MTEL Math: Complex Numbers
- MTEL Math: Properties of Numbers
- MTEL Math: Exponents & Exponential Expressions
- MTEL Math: Roots & Radical Expressions
- MTEL Math: Scientific Notation
- MTEL Math: Number Theory
- MTEL Math: Number Patterns & Sequences
- MTEL Math: Number Patterns & Series
- MTEL Math: Properties of Functions
- MTEL Math: Graphing Functions
- MTEL Math: Factoring
- MTEL Math: The Coordinate Graph & Symmetry
- MTEL Math: Linear Equations
- MTEL Math: Systems of Linear Equations
- MTEL Math: Introduction to Quadratics
- MTEL Math: Working with Quadratic Functions
- MTEL Math: Polynomial Functions Basics
- MTEL Math: Higher-Degree Polynomial Functions
- MTEL Math: Piecewise, Absolute Value & Step Functions
- MTEL Math: Rational Expressions, Functions & Graphs
- MTEL Math: Exponential & Logarithmic Functions
- MTEL Math: Measurement
- MTEL Math: Perimeter & Area
- MTEL Math: Polyhedrons & Geometric Solids
- MTEL Math: Symmetry, Similarity & Congruence
- MTEL Math: Properties of Lines
- MTEL Math: Angles
- MTEL Math: Triangles
- MTEL Math: Triangle Theorems & Proofs
- MTEL Math: Similar Polygons
- MTEL Math: The Pythagorean Theorem
- MTEL Math: Quadrilaterals
- MTEL Math: Circles
- MTEL Math: Circular Arcs & Measurement
- MTEL Math: Analytic Geometry & Conic Sections
- MTEL Math: Polar Coordinates & Parameterization
- MTEL Math: Transformations
- MTEL Math: Data & Graphs
- MTEL Math: Statistics
- MTEL Math: Data Collection
- MTEL Math: Samples & Populations
- MTEL Math: Probability
- MTEL Math: Trigonometric Functions
- MTEL Math: Graphs of Trigonometric Functions
- MTEL Math: Trigonometric Identities
- MTEL Math: Applications of Trigonometry
- MTEL Math: Limits
- MTEL Math: Continuity
- MTEL Math: Rate of Change
- MTEL Math: Derivative Calculations & Rules
- MTEL Math: Graphing Derivatives & L'Hopital's Rule
- MTEL Math: Area Under the Curve & Integrals
- MTEL Math: Integration Techniques
- MTEL Math: Integration Applications
- MTEL Math: Differential Equations
- MTEL Math: Discrete & Finite Math
- MTEL Mathematics Flashcards