ALEX Classroom Resource

  

Precalculus and Advanced Topics Module 2, Topic B: Linear Transformations of Planes and Space

  Classroom Resource Information  

Title:

Precalculus and Advanced Topics Module 2, Topic B: Linear Transformations of Planes and Space

URL:

https://www.engageny.org/resource/precalculus-and-advanced-topics-module-2-topic-b-overview

Content Source:

EngageNY
Type: Lesson/Unit Plan

Overview:

Module 2, Topic B explores the geometric context for higher-dimensional matrices. The geometric effect of matrix operations—matrix product, matrix sum, and scalar multiplication—are examined, and students come to see, geometrically, that matrix multiplication for square matrices is not a commutative operation, but that it still satisfies the associative and distributive properties. The geometric and arithmetic roles of the zero matrices and identity matrix are discussed, and students see that a multiplicative inverse to a square matrix exists precisely when the determinant of the matrix is non-zero.

Note: This module is identified as Precalculus and Advanced Topics in the EngageNY curriculum. It also corresponds to the Algebra II and Algebra II with Trigonometry Alabama Course of Study.

Content Standard(s):
Mathematics
MA2015 (2016)
Grade: 9-12
Precalculus
10 ) (+) 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. [N-VM11]

Mathematics
MA2015 (2016)
Grade: 9-12
Algebra II
8 ) (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. [N-VM7]

Mathematics
MA2015 (2016)
Grade: 9-12
Algebra II
9 ) (+) Add, subtract, and multiply matrices of appropriate dimensions. [N-VM8]

Mathematics
MA2015 (2016)
Grade: 9-12
Algebra II
10 ) (+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. [N-VM9]

Mathematics
MA2015 (2016)
Grade: 9-12
Algebra II
11 ) (+) 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. [N-VM10]

Mathematics
MA2015 (2016)
Grade: 9-12
Algebra II with Trigonometry
8 ) (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. [N-VM7]

Mathematics
MA2015 (2016)
Grade: 9-12
Algebra II with Trigonometry
9 ) (+) Add, subtract, and multiply matrices of appropriate dimensions. [N-VM8]

Mathematics
MA2015 (2016)
Grade: 9-12
Algebra II with Trigonometry
10 ) (+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. [N-VM9]

Mathematics
MA2015 (2016)
Grade: 9-12
Algebra II with Trigonometry
11 ) (+) 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. [N-VM10]

Tags: add, addition, associative, commutative, distributive, identity matrix, inverse, multiplication, multiply, real numbers, scalar, square matrix, subtract, zero matrix
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Comments

There are ten lessons on this topic.

This resource is free for teachers to access and use. All resources required for the lessons are available to print from the site. 

Note: This module is identified as Precalculus and Advanced Topics in the EngageNY curriculum. It also corresponds to the Algebra II and Algebra II with Trigonometry Alabama Course of Study.

  This resource provided by:  
Author: Hannah Bradley