About This Chapter
Working with Matrices & Determinants - Chapter Summary
High school students need to read and understand a great deal of information both before they graduate and as they move on in college or the professional world. This chapter provides students with focused training on developing their understanding of matrices and determinants.
Instead of an endless chapter of information, the chapter has been divided into short, individualized lessons. Students have the option to review all of the lessons in order, but they can also pick and choose lesson topics in which they need the most assistance. The chapter menu provides a list of all lessons available, and since each lesson is only focused on a single topic, students can easily find what they need. After completing this chapter, students will be ready to:
- Solve inverse matrices
- Solve linear systems using Gaussian and Gauss-Jordan elimination
- Solve inconsistent and dependent systems using Gaussian elimination
- Use determinants to solve systems of linear equations in two and three variables
- Use Cramer's Rule with inconsistent and dependent systems
- Evaluate higher-order determinants in algebra
1. 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.
2. 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.
3. 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.
4. Inconsistent and Dependent Systems: Using Gaussian Elimination
Watch this video lesson to learn whether or not you can use Gaussian elimination to solve inconsistent and dependent systems. Also, learn whether there is another way to find solutions of these systems.
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. 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.
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.
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Other chapters within the High School Precalculus: Homeschool Curriculum course
- Graphing with Functions Review
- Working With Inequalities Review
- Absolute Value Equations Review
- Working with Complex Numbers Review
- Quadratic Functions Review
- Solving & Graphing Quadratic Functions
- Polynomial Functions Review
- Working with Polynomial Functions
- Graphing Piecewise Functions
- Graph Symmetry
- Rate of Change
- Rational Functions & Difference Quotients
- Rational Expressions & Equations Review
- Graphing Rational Functions
- Exponential & Logarithmic Functions Review
- Working with Exponential & Logarithmic Functions
- Trigonometric Functions & Graphs Review
- Solving Trigonometric Identities
- Trigonometric Graphs & Applications
- Understanding Vectors, Matrices & Determinants
- Mathematical Sequences & Series Review
- Sets in Algebra
- Analytic Geometry & Conic Sections Review
- Polar Coordinates and Parameterizations
- Precalculus: Homeschool Assignments & Projects
- Homeschool Resources for Precalculus in High School