# Ch 28: Vectors, Matrices & Determinants in Trigonometry: Help and Review

### About This Chapter

## Who's it for?

Anyone who needs help learning or mastering high school trigonometry material will benefit from taking this course. There is no faster or easier way to learn high school trigonometry. Among those who would benefit are:

- Students who have fallen behind in understanding how matrices and their determinants can be used to solve systems of linear equations
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about vectors, matrices and determinants
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources

## How it works:

- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the Vectors, Matrices & Determinants in Trigonometry chapter exam.

## Why it works:

**Study Efficiently**: Skip what you know, review what you don't.**Retain What You Learn**: Engaging animations and real-life examples make topics easy to grasp.**Be Ready on Test Day**: Use the Vectors, Matrices & Determinants in Trigonometry chapter exam to be prepared.**Get Extra Support**: Ask our subject-matter experts any vectors, matrices and determinants question. They're here to help!**Study With Flexibility**: Watch videos on any web-ready device.

## Students will review:

This chapter helps students review the concepts in a vectors, matrices and determinants unit of a standard high school trigonometry course. Topics covered include:

- Performing operations on vectors in the plane
- Applying the dot product of vectors
- Writing augmented matrices
- Performing matrix row operations
- Adding, subtracting and multiplying matrices
- Solving linear systems using inverse matrices
- Using Gaussian elimination to solve linear systems
- Solving linear systems using Gauss-Jordan elimination
- Solving inconsistent and dependent linear systems
- Determining the multiplicative inverse of a square matrix
- Taking the determinant of a matrix
- Solving linear systems in two or three variables using determinants
- Using Cramer's rule with inconsistent and dependent systems
- Evaluating higher-order determinants

### 1. What is a Matrix?

A matrix is an array of numbers enclosed in brackets that represents a system of equations. Explore matrices and the parts of a matrix and learn how to add, subtract, and multiply matrices.

### 2. How to Solve Linear Systems Using Gaussian Elimination

In mathematics, Gaussian elimination is a process used to solve equations by removing the variables step-by-step. Learn how to solve linear systems using Gaussian elimination. Also, explore linear systems and an augmented matrix to understand the process for solving the system.

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

Using Gauss-Jordan elimination to solve linear systems involves changing the matric into a reduced row echelon form. Learn about linear systems, the Gauss-Jordan elimination method, and solving for the final solution through the reduced row echelon form.

### 4. Multiplicative Inverses of Matrices and Matrix Equations

The multiplicative inverse of matrices states that matrix identify can be determined by multiplying a matrix with its multiplicative inverse. Learn how to use the matrix multiplicative inverse to solve matrix equations through a series of examples.

### 5. How to Take a Determinant of a Matrix

The determinant is a simple but unique operation you can perform with a matrix. Learn how to solve for the determinant based on the size of the matrix, and study explanations of each type of matrix to expand your math vocabulary.

### 6. Resultant Vector: Definition & Formula

The resultant vector is the vector sum of two or more vectors being combined. Learn about the definition of a resultant vector and solve the example problems in finding the resultant vector.

### 7. Singular Matrix: Definition, Properties & Example

A singular matrix does not have an inverse and is a '2 x 2' matrix with two rows and two columns. In this lesson, explore the definition, operations, and properties of matrices, and apply your understanding through examples.

### Earning College Credit

Did you know… We have over 220 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

### Other Chapters

Other chapters within the High School Trigonometry: Help and Review course

- Real Numbers - Types and Properties: Help and Review
- Working with Linear Equations in Trigonometry: Help and Review
- Working with Inequalities in Trigonometry: Help and Review
- Absolute Value Equations in Trigonometry: Help and Review
- Working with Complex Numbers in Trigonometry: Help and Review
- Systems of Linear Equations in Trigonometry: Help and Review
- Mathematical Modeling in Trigonometry: Help and Review
- Introduction to Quadratics in Trigonometry: Help and Review
- Working with Quadratic Functions in Trigonometry: Help and Review
- Coordinate Geometry Review: Help and Review
- Functions for Trigonometry: Help and Review
- Understanding Function Operations in Trigonometry: Help and Review
- Graph Symmetry in Trigonometry: Help and Review
- Graphing with Functions in Trigonometry: Help and Review
- Basic Polynomial Functions in Trigonometry: Help and Review
- Higher-Degree Polynomial Functions in Trigonometry: Help and Review
- Rational Functions in Trigonometry: Help and Review
- Trig - Rational Expressions & Function Graphs: Help & Review
- Exponential & Logarithmic Functions in Trigonometry: Help and Review
- Trigonometric Functions: Help and Review
- Geometry in Trigonometry: Help and Review
- Triangle Trigonometry: Help and Review
- Working with Trigonometric Graphs: Help and Review
- Trigonometric Equations: Help and Review
- Working with Trigonometric Identities: Help and Review
- Applications of Trigonometry: Help and Review
- Analytic Geometry & Conic Sections in Trigonometry: Help and Review
- Polar Coordinates & Parameterizations: Help and Review
- Circular Arcs, Circles & Angles: Help and Review
- TASC Math: Trigonometry