About This Chapter
Standard: Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network (CCSS.Math.Content.HSN-VM.C.6).
Standard:Multiply matrices by scalars to produce new matrices, e.g., as when all the payoffs in a game are doubled (CCSS.Math.Content.HSN-VM.C.7) .
Standard:Add, subtract and multiply matrices of appropriate dimensions (CCSS.Math.Content.HSN-VM.C.8) .
Standard:Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties (CCSS.Math.Content.HSN-VM.C.9).
Standard:Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse (CCSS.Math.Content.HSN-VM.C.10).
Standard:Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors (CCSS.Math.Content.HSN-VM.C.11).
Standard:Work with 2 x 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area (CCSS.Math.Content.HSN-VM.C.12).
About This Chapter
A matrix is an array of numbers arranged into a set number of rows and columns, for example, 3 x 3 or 4 x 2. Students with an understanding of this common core standard will be able to use matrices to represent data and to determine sums, differences and products of the numbers in a matrix. Learning about matrices can be especially beneficial for students who are interested in computer programming.
Lessons in this standard cover the following:
- Multiplying a matrix by a scalar
- Adding, subtracting and multiplying matrices
- Properties of matrix multiplication
- Vectors and matrices
- Zero and identity matrices
- Matrices as transformations of a plane
- Taking a determinant of a matrix
- Determinants and area
Students who have mastered this standard should be able to add, subtract and multiply matrices and determine the absolute value of a determinant. They also should understand the difference between matrix multiplication and multiplication of numbers, as well as the role of zero and identity matrices in matrix addition and multiplication.
How to Use These Lessons in Your Classroom
Following are some tips on using these lessons on matrices as part of your curriculum to help students meet common core standards for mathematics:
Watch the video lesson What is a Matrix? in class or assign it as homework to introduce students to the basic concept and arrangement of matrices.
Adding and Subtracting Matrices Lesson
Have each student create a matrix based on characteristics of classmates, such as eye color or hair color. Then, have the students use their matrices to determine factors such as which is most popular eye color or how many more students have brown eyes than blue.
Pre- and Post-Quizzes
Have students take the quiz for How to Take a Determinant of a Matrix to gauge their initial aptitude for calculating determinants. Then, have them watch the video lesson and retake the quiz to see if their comprehension has improved.
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 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!
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