# Ch 10: Matrices & Determinants in Algebra II Lesson Plans

### About This Chapter

## Weekly Syllabus

Below is a sample breakdown of the Matrices & Determinants chapter into a 5-day school week. Based on the pace of your course, you may need to adapt the lesson plan to fit your needs.

Day | Topics | Key Terms and Concepts Covered |
---|---|---|

Monday | Matrices overview Augmented matrix Row operations | Definition of matrix; Writing an augmented matrix for a linear system; Performing row operations |

Tuesday | Notations and operations Inverse matrices Solving linear systems | Matrix notation, equal matrices and math operations; Solving inverse matrices; Solving linear systems using Gaussian and Gauss-Jordan eliminations |

Wednesday | Gaussian elimination Multiplication inverses | Applying Gaussian elimination to inconsistent and dependent systems; Using inverses to solve matrix equations |

Thursday | Determinants | Taking a determinant of a matrix; Using determinants to solve systems of linear equations with two or three variables |

Friday | Cramer's Rule Higher-order determinants | Using determinants to find inconsistent and dependent systems; Evaluating higher-order determinants |

### 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. How to Write an Augmented Matrix for a Linear System

Watch this video lesson to learn how you can turn your system of equations into matrix form. The matrix form is another way of writing your linear system that is sometimes easier to work with.

### 3. 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.

### 4. 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.

### 5. 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.

### 6. 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.

### 7. 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.

### 8. 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.

### 9. 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.

### 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!

### 11. 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.

### 12. 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.

### 13. 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.

### 14. 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

Other chapters within the Algebra II Curriculum Resource & Lesson Plans course

- Basic Arithmetic in Algebra II Lesson Plans
- Algebraic Expressions & Equations Lesson Plans
- Real Numbers in Algebra II Lesson Plans
- Complex & Imaginary Numbers in Algebra Lesson Plans
- Exponents & Exponential Expressions in Algebra Lesson Plans
- Properties of Functions in Algebra Lesson Plans
- Linear Equations in Algebra Lesson Plans
- Systems of Linear Equations in Algebra II Lesson Plans
- Working with Inequalities in Algebra Lesson Plans
- Absolute Value Review in Algebra II Lesson Plans
- Polynomials in Algebra II Lesson Plans
- Factoring in Algebra II Lesson Plans
- Quadratic Equations in Algebra II Lesson Plans
- Rational Expressions in Algebra II Lesson Plans
- Graphing & Functions in Algebra II Lesson Plans
- Roots & Radical Expressions in Algebra II Lesson Plans
- Exponential & Logarithmic Functions: Lesson Plans
- Conic Sections in Algebra II Lesson Plans
- Sequence & Series in Algebra II Lesson Plans
- Sets in Algebra II Lesson Plans
- Combinatorics in Algebra II Lesson Plans
- Lesson Plans for Calculations, Ratios, Percent & Proportions
- Statistics in Algebra II Lesson Plans
- Trigonometry in Algebra II Lesson Plans