Classroom Resources (2) |

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

[MA2015] AL2 (9-12) 8 :

[MA2015] AL2 (9-12) 9 :

[MA2015] AL2 (9-12) 10 :

[MA2015] AL2 (9-12) 11 :

[MA2015] ALT (9-12) 8 :

[MA2015] ALT (9-12) 9 :

[MA2015] ALT (9-12) 10 :

[MA2015] ALT (9-12) 11 :

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]

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 :

[MA2015] AL2 (9-12) 9 :

[MA2015] AL2 (9-12) 10 :

[MA2015] AL2 (9-12) 11 :

[MA2015] ALT (9-12) 9 :

[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]

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 :

[MA2015] ALT (9-12) 11 :

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.**