# Ch 20: MTTC Math (Secondary): Vectors, Matrices & Determinants

### About This Chapter

## MTTC Math (Secondary): Vectors, Matrices & Determinants - Chapter Summary

In this chapter, you can review what you need to know about solving mathematical problems with vectors, matrices, linear systems and determinants for the Michigan Test for Teacher Certification (MTTC) Mathematics (Secondary) exam. This series of engaging lesson videos helps you brush up on:

- Operations on vectors in the coordinate plane
- Applications of the dot product of vectors
- Augmented matrices and matrix row operations
- Matrix notation, equal matrices and operations with matrices
- Inverse matrices and linear systems and Gaussian elimination
- Gauss-Jordan elimination with linear systems
- Inconsistent vs. dependent systems with Cramer's rule and Gaussian elimination
- Multiplicative inverses
- Linear equations with two and three variables
- Higher-order determinants

If, at any time, you become confused about any of the subjects in this chapter, you can contact our instructors for help. Reinforce your retention of these lessons by completing the assessment quizzes that accompany them. These assessments also allow you to determine what topics you don't understand. Return to the lesson videos to fortify your understanding of these areas with video tags and lesson transcripts.

### MTTC Math (Secondary): Vectors, Matrices & Determinants - Chapter Objectives

You will need to take the MTTC Mathematics (Secondary) as part of the licensure process for teaching secondary math in the state of Michigan. This certification exam is composed of 80 multiple-choice questions and administered in a either a computer or paper-based format.

The material covered by the exam is broken down into four domains including: Mathematical Processes and Number Concepts (making up 22% of the exam), Patterns, Algebraic Relationships and Functions (28%), Measurements and Geometry (22%) and Data Analysis, Statistics, Probability and Discrete Mathematics (28%). You can expect to see a few questions in all four of these domains about vectors, matrices and/or determinants. This chapter has been assembled to aid in your review of these topics so that you can improve your skills for test day.

### 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. How to Solve Linear Systems Using Gauss-Jordan Elimination

You will come across simple linear systems and more complex ones as you progress in math. Watch this video lesson to learn how you can use Gauss-Jordan elimination to help you solve these linear 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. 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.

### 15. 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.

### Earning College Credit

Did you know… We have over 200 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

### Transferring credit to the school of your choice

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.

### Other Chapters

Other chapters within the MTTC Mathematics (Secondary) (022): Practice & Study Guide course

- MTTC Math (Secondary): Reasoning & Problem Solving
- MTTC Math (Secondary): Basic Arithmetic
- MTTC Math (Secondary): Absolute Value
- MTTC Math (Secondary): Integers
- MTTC Math (Secondary): Introduction to Fractions
- MTTC Math (Secondary): Operations with Fractions
- MTTC Math (Secondary): Introduction to Decimals
- MTTC Math (Secondary): Operations with Decimals
- MTTC Math (Secondary): Percents
- MTTC Math (Secondary): Estimating & Rounding
- MTTC Math (Secondary): Rational & Irrational Numbers
- MTTC Math (Secondary): Complex Numbers
- MTTC Math (Secondary): Properties of Real Numbers
- MTTC Math (Secondary): Exponents & Exponential Expressions
- MTTC Math (Secondary): Roots & Radical Expressions
- MTTC Math (Secondary): Scientific Notation
- MTTC Math (Secondary): Number Theory
- MTTC Math (Secondary): Ratios & Rates
- MTTC Math (Secondary): Proportions
- MTTC Math (Secondary): Sequences
- MTTC Math (Secondary): Series
- MTTC Math (Secondary): Factoring
- MTTC Math (Secondary): Properties of Functions
- MTTC Math (Secondary): Graphing Functions
- MTTC Math (Secondary): The Coordinate Graph & Graph Symmetry
- MTTC Math (Secondary): Linear Equations
- MTTC Math (Secondary): Systems of Equations
- MTTC Math (Secondary): Inequalities
- MTTC Math (Secondary): Quadratic Equations
- MTTC Math (Secondary): Working with Quadratic Equations
- MTTC Math (Secondary): Polynomial Functions
- MTTC Math (Secondary): Higher-Degree Polynomial Functions
- MTTC Math (Secondary): Piecewise Functions
- MTTC Math (Secondary): Rational Expressions & Functions
- MTTC Math (Secondary): Exponential & Logarithmic Functions
- MTTC Math (Secondary): Trigonometric Functions
- MTTC Math (Secondary): Solving Trigonometric Equations
- MTTC Math (Secondary): Limits
- MTTC Math (Secondary): Continuity of a Function
- MTTC Math (Secondary): Rate of Change & Derivatives
- MTTC Math (Secondary): Calculating Derivatives & Derivative Rules
- MTTC Math (Secondary): Graphing Derivatives & L'Hopital's Rule
- MTTC Math (Secondary): Applications of Derivatives
- MTTC Math (Secondary): Area Under the Curve & Integrals
- MTTC Math (Secondary): Integration & Integration Techniques
- MTTC Math (Secondary): Integration Applications
- MTTC Math (Secondary): Differential Equations
- MTTC Math (Secondary): Units & Systems of Measurement
- MTTC Math (Secondary): Perimeter & Area
- MTTC Math (Secondary): Polyhedrons & Geometric Solids
- MTTC Math (Secondary): Symmetry, Similarity & Congruence
- MTTC Math (Secondary): Points, Lines & Angles
- MTTC Math (Secondary): Triangles
- MTTC Math (Secondary): Triangle Theorems & Proofs
- MTTC Math (Secondary): Similar Triangles & Polygons
- MTTC Math (Secondary): The Pythagorean Theorem
- MTTC Math (Secondary): Quadrilaterals
- MTTC Math (Secondary): Circles
- MTTC Math (Secondary): Circular Arcs & Measurement
- MTTC Math (Secondary): Conic Sections
- MTTC Math (Secondary): Polar Coordinates & Parametric Equations
- MTTC Math (Secondary): Transformations
- MTTC Math (Secondary): Types of Graphs, Tables, & Data
- MTTC Math (Secondary): Data & Statistics
- MTTC Math (Secondary): Collecting & Analyzing Data
- MTTC Math (Secondary): Samples & Populations in Research
- MTTC Math (Secondary): Probability
- MTTC Math (Secondary): Discrete & Finite Math
- MTTC Mathematics (Secondary) Flashcards