# Ch 24: Performing Operations on Matrices & Vectors

### About This Chapter

## Performing Operations on Matrices & Vectors - Chapter Summary

This chapter contains a thorough analysis of the concepts of vectors and matrices, including explanations of how to perform operations of a matrix and vector. The video lessons include definitions, types, scalar multiplication, formulas, and how to perform operations and examples. By the end of this chapter, you should be able to:

- Define vector, matrices, and scalar
- Perform vector operations from a geometric approach
- Provide an appropriate formula & examples of a vector
- Perform matrix row operations
- Construct a matrix notation, equal matrices & math operations
- Solve multiplicative inverses of matrices and matrix equations
- Calculate a determinant of a matrix

The video lessons in this chapter are presented in manageable pieces for you to quickly assess your understanding of the ideas on matrices and vectors. All the lessons are taught by professional mathematics instructors, and you'll also have access to self-assessment quizzes and transcripts of all the video lessons. Through your Dashboard, you can track your progress through the chapter.

### 1. What Is a Vector? - Definition & Types

After watching this lesson, you will be able to explain what vectors are in physics, give some examples of vectors and have a basic idea of how they can be manipulated mathematically. A short quiz will follow.

### 2. Vector Addition (Geometric Approach): Explanation & Examples

After watching this video, you will be able to explain why we might need to add two vectors and, given magnitudes and directions, add two vectors using geometric methods. A short quiz will follow.

### 3. Vector Subtraction (Geometric): Formula & Examples

After watching this lesson, you will be able to subtract vectors geometrically and give examples of how that process might be used in physics. A short quiz will follow.

### 4. Scalar Multiplication of Vectors: Definition & Calculations

After watching this video, you will be able to explain what scalar multiplication is and complete basic calculations involving the scalar multiplication of vectors. A short quiz will follow.

### 5. 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.

### 6. 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.

### 7. 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.

### 8. 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.

### 9. 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.

### 10. 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!

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### Other Chapters

Other chapters within the NES Mathematics Middle Grades & Early Secondary (105): Practice & Study Guide course

- Overview of Mathematical Reasoning
- Introduction to Mathematical Problem Solving
- NES Math: Properties of Real Numbers
- Understanding Relations & Functions
- Overview of Linear Functions & Equations
- Quadratic Equations, Functions & Inequalities
- Overview of Polynomial Equations, Functions & Inequalities
- Working with Absolute Values
- Overview of Rational & Radical Functions
- NES Math: Piecewise Functions
- NES Math: Exponential & Logarithmic Functions
- Scientific Measurement Principles & Calculations
- NES Math: Foundations of Geometry
- NES Math: Geometric Figures
- Triangle Properties & Proofs
- NES Math: Parallel Lines & Polygons
- NES Math: Circles & Arc of a Circle
- NES Math: Conic Sections
- NES Math: Geometric Solids
- NES Math: Analytical Geometry
- Statistics: Principles & Techniques
- Probability: Principles & Techniques
- Overview of Discrete Mathematics
- Solving Problems with Sequences & Series
- NES Mathematics Middle Grades & Early Secondary Flashcards