Standard 3 : Perform operations on matrices and use matrices in applications. (Archived)



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General Information

Number: MAFS.912.N-VM.3
Title: Perform operations on matrices and use matrices in applications.
Type: Cluster
Subject: Mathematics - Archived
Grade: 912
Domain-Subdomain: Number & Quantity: Vector & Matrix Quantities

Related Standards

This cluster includes the following benchmarks
Code Description
MAFS.912.N-VM.3.6: Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
MAFS.912.N-VM.3.7: Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
MAFS.912.N-VM.3.8: Add, subtract, and multiply matrices of appropriate dimensions.
MAFS.912.N-VM.3.9: Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
MAFS.912.N-VM.3.10: Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
MAFS.912.N-VM.3.11: 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.
MAFS.912.N-VM.3.12: Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.


Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Lesson Plans

Name Description
Having Fun with Matrix Multiplication:

In this lesson, students learn how to multiply matrices using paper-and-pencil and GeoGebra. Students will use matrix multiplication to represent and solve real-world problems.

Using matrices to model the dynamics of demography:

In this lesson, students will formulate, implement, and interpret a simple demographic model in which birth rates and survival rates are constant for each age cohort. The model will have the form x'=Ax, where x is the population distribution at some time, x' the population 20 years later, and A a (Leslie) matrix that contains the problem parameters. Using a context should help students better understand the meaning of matrix multiplication and its role in linear discrete dynamics.

Perspectives Video: Professional/Enthusiasts

Name Description
Hacking the Matrices (in your Kinect) for Real-Time 3D Scanning:

What's the point to learning about matrices? You can hack gaming devices for off-the-shelf real time 3D visualization!

Download the CPALMS Perspectives video student note taking guide.

Making Color with Matrices:

Did you know that computers use matrices to represent color? Learn how computer graphics work in this video.

Presentation/Slideshow

Name Description
Matrices:

This resource is a PowerPoint presentation and a form for guided note taking to be used while viewing the presentation about Matrix Operations. It begins by defining matrices and identifying types of matrices. It then goes into how to add, subtract, and multiply matrices, including how to use scalar multiplication. The final portion deals with finding the determinants of 2x2 and 3x3 matrices and Inverse Matrices.



Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

Perspectives Video: Professional/Enthusiasts

Title Description
Hacking the Matrices (in your Kinect) for Real-Time 3D Scanning:

What's the point to learning about matrices? You can hack gaming devices for off-the-shelf real time 3D visualization!

Download the CPALMS Perspectives video student note taking guide.

Making Color with Matrices:

Did you know that computers use matrices to represent color? Learn how computer graphics work in this video.

Presentation/Slideshow

Title Description
Matrices:

This resource is a PowerPoint presentation and a form for guided note taking to be used while viewing the presentation about Matrix Operations. It begins by defining matrices and identifying types of matrices. It then goes into how to add, subtract, and multiply matrices, including how to use scalar multiplication. The final portion deals with finding the determinants of 2x2 and 3x3 matrices and Inverse Matrices.



Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this topic.

Perspectives Video: Professional/Enthusiasts

Title Description
Hacking the Matrices (in your Kinect) for Real-Time 3D Scanning:

What's the point to learning about matrices? You can hack gaming devices for off-the-shelf real time 3D visualization!

Download the CPALMS Perspectives video student note taking guide.

Making Color with Matrices:

Did you know that computers use matrices to represent color? Learn how computer graphics work in this video.