About This Chapter
Solving Matrices & Determinants - Chapter Summary
In this chapter, you will learn about systems of equations and the many types of matrices that exist in the mathematical world. Our instructors will define reduced row-echelon forms and explain how to take a determinant of a matrix. Your study will continue with steps to solve systems of linear equations in two and three variables using determinants.
As you progress through the chapter, you will review matrix notation, and learn how to use rules to take the determinant of any size matrix. These lessons will teach you how to:
- Differentiate between and identify the different kinds of matrices
- Define reduced row-echelon form
- Take the determinant of a matrix
- Solve systems of linear equations using Cramer's Rule
- Explain the math operations you can do with matrices
- Use rules to work with higher-order determinants
- Solve inverse matrices
- Give examples of adjugate matrices
Use our chapter tests and lesson quizzes to gauge how well you understand the subject matter and where you may want to focus additional study. These materials are designed by professional instructors to ensure your learning experience is easy and engaging. If you need help as you work through the lessons, contact one of our instructors for assistance. All our lessons and quizzes are available to you anytime, and you can print the quizzes and transcripts for offline study.
1. What is a System of Equations?
So what happens if we want to compare more than one equation? Welcome to a 'system' of equations! Learn what one is, how to solve them and when they come up in real life.
2. Types of Matrices: Definition & Differences
Matrices are rectangular arrays of numbers arranged in the form of rows and columns. In this lesson, you will explore the various types of matrices with examples of each.
3. Reduced Row-Echelon Form: Definition & Examples
In this lesson, we'll look at one of the most useful forms of a matrix: the reduced row-echelon form. We'll review the definition of reduced row-echelon form and look at several examples.
4. 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!
5. 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.
6. 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.
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. 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.
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. Adjugate Matrix: Definition, Formation & Example
In this lesson we'll calculate the adjugate matrix. This will require finding minors, determinants, and transposes. All of these steps will be carefully explained with an example.
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Other chapters within the NDA Exam Preparation & Study Guide course
- About the NDA Exam
- Algebra Concepts
- Advanced Algebra Concepts
- Trigonometry Concepts
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- Analytic Geometry
- Functions, Limits & Continuity
- Derivative Rules
- Calculations & Applications of Derivatives
- Integral Calculus
- Differential Equations & Applications
- Scalars & Vectors in Algebra
- Visualizing Statistics
- Probability Concepts in Math
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