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ALEX Classroom Resources  
   View Standards     Standard(s): [MA2015] PRE (9-12) 10 :
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]

[MA2015] AL2 (9-12) 8 :
8 ) (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. [N-VM7]

[MA2015] AL2 (9-12) 9 :
9 ) (+) Add, subtract, and multiply matrices of appropriate dimensions. [N-VM8]

[MA2015] AL2 (9-12) 10 :
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]

[MA2015] AL2 (9-12) 11 :
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]

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

[MA2015] ALT (9-12) 9 :
9 ) (+) Add, subtract, and multiply matrices of appropriate dimensions. [N-VM8]

[MA2015] ALT (9-12) 10 :
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]

[MA2015] ALT (9-12) 11 :
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]

Subject: Mathematics (9 - 12)
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
Description:

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.



   View Standards     Standard(s): [MA2015] PRE (9-12) 10 :
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]

[MA2015] AL2 (9-12) 9 :
9 ) (+) Add, subtract, and multiply matrices of appropriate dimensions. [N-VM8]

[MA2015] AL2 (9-12) 10 :
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]

[MA2015] AL2 (9-12) 11 :
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]

[MA2015] ALT (9-12) 9 :
9 ) (+) Add, subtract, and multiply matrices of appropriate dimensions. [N-VM8]

[MA2015] ALT (9-12) 10 :
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]

[MA2015] ALT (9-12) 11 :
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]

Subject: Mathematics (9 - 12)
Title: Precalculus and Advanced Topics Module 2, Topic E: First-Person Video Games--Projection Matrices
URL: https://www.engageny.org/resource/precalculus-and-advanced-topics-module-2-topic-e-overview
Description:

In Module 2, Topic E students apply the knowledge developed in this module to understand how first-person video games use matrix operations to project three-dimensional objects onto two-dimensional screens and animate those images to give the illusion of motion.

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.



ALEX Classroom Resources: 2

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