About This Chapter
Standard: Represent a system of linear equations as a single matrix equation in a vector variable. (CCSS.Math.Content.HSA-REI.C.8)
Standard: Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3x3 or greater). (CCSS.Math.Content.HSA-REI.C.9)
About This Chapter
Students who have mastered these standards understand that a matrix is a group of numbers set up within a specific amount of columns and rows. They're also able to perform the addition, multiplication and subtraction of matrices. Masters of the matrix standards know the relationship between vectors and matrices as well as understand matrix arithmetic.
Lessons in this standard cover concepts such as:
- Finding the inverse of a 2x2 matrix
- Solving a system of equations with an inverse
- Representing a system of equations by using matrices
- Working with zero and identity matrices
Students demonstrate mastery of these standards when they're able to efficiently display linear algebraic equations as matrices. They also solve systems of equations with different types of matrices that can come in various sizes. Since matrices are the focus of the linear algebra branch of mathematics, mastery of these standards can support students in various mathematic and scientific careers outside of high school and college.
How to Use These Lessons in Your Classroom
Here are some tips for how to use the lessons to support instruction in these standards:
Matrix Introduction Lessons
Develop a worksheet that consists of questions about matrix vocabulary and basic matrix calculations. Have your class watch the video lesson 'What is a Matrix?' and pass out the worksheet for homework. The next day, have a discussion with your students about the correct answers. Clear up any questions or issues regarding the lesson. Make sure the class is on the same page before moving on.
Adding, Subtracting and Multiplying Matrices Lessons
After displaying the video lessons regarding subtracting, adding and multiplying matrices, fill the chalkboard with various matrix problems. Go over a few examples to ensure your students understand how to complete each operation. Call on students to come up to the chalkboard to answer the remaining problems. When a student answers a problem incorrectly, go through each step to clarify any issues.
Pre-Quiz and Post-Quiz Lessons
In class, require your students to work through the quizzes for all the lessons in this chapter. After the matrix concepts are introduced to the students, take a few days to go over the lessons thoroughly with your class. When you finish teaching the class about matrices, have them take the video lesson quizzes again to see how they understood the materials.
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Other chapters within the Common Core Math - Algebra: High School Standards course
- Common Core HS Algebra: Algebraic Expressions
- Common Core HS Algebra: Linear Equations
- Common Core HS Algebra: Linear Inequalities
- Common Core HS Algebra: Quadratics
- Common Core HS Algebra: Exponents and Exponential Functions
- Common Core HS Algebra: Polynomials
- Common Core HS Algebra: Rational and Radical Expressions and Equations
- Common Core HS Algebra: Systems of Equations
- Common Core HS Algebra: Sequences and Series
- Understanding Common Core Standards