About This Chapter
Introduction to Matrices - Chapter Summary
This comprehensive introduction to matrices closely examines matrix forms, how to perform mathematic operations between two matrices and how to calculate the eigenvectors of a matrix. Review the entertaining lessons in this chapter at your own pace. When finished, you will be able to:
- Define a matrix and cofactor
- Describe the properties and application of scalars and matrices
- Compare and contrast the square matrix and identity matrix
- Exhibit knowledge of matrix equations and multiple inverses of matrices
- Simplify and solve linear systems by using matrix row operations
- Determine the eigenvectors of a matrix
- Define diagonal and symmetric matrices and diagonalize a symmetric matrix
This chapter is designed to accommodate your unique study needs and personal schedule. Feel free to access the lessons any time via your computer or mobile device, and review them in any order and as often as you'd like. Use our multiple-choice quizzes and chapter exam to find out how much you understand about matrices. Our Dashboard tracks your progress through this chapter and lets you send any questions about specific lesson topics to our experts.
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.
2. Cofactor: Definition & Formula
In this lesson, we'll use step-by-step instructions to show you how to how to find the cofactor of a matrix. We'll begin with the definition of a cofactor, after which you'll learn how to use the formula and perform your own calculations.
3. Scalars & Matrices: Properties & Application
In this lesson, we will review what a matrix is and what a scalar is. After we've done this, we will discuss scalar multiplication and look at an application involving this type of multiplication. We'll finish up by looking at the properties of scalar multiplication.
4. Square Matrix: Definition & Concept
A square matrix is a special type of matrix with an equal number of rows and columns. Learn more about square matrices in this lesson, including how to add and multiply them. Then, test your understanding with a short quiz.
5. Identity Matrix: Definition & Properties
In this lesson, we will learn about the identity matrix, which is a square matrix that has some unique properties. We will discover that a given matrix may have more than one identity matrix.
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.
7. Row Operations & Reductions with Augmented Matrices
If you've ever managed to get hopelessly lost trying to solve a three-variable, three-equation linear system, then this lesson might help a lot. In this lesson, we'll explore how to use matrix row operations to simplify and solve linear systems.
8. How to Determine the Eigenvectors of a Matrix
In this lesson, you'll explore the subject of eigenvectors. After learning what an eigenvector is in concept, we'll solidify in your mind how to find them by working through an example problem together.
9. Diagonalizing Symmetric Matrices: Definition & Examples
In this lesson, we define symmetric and diagonal matrices. We then use eigenvalues and eigenvectors to form a very special matrix which is then used to diagonalize a symmetric matrix.
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