ALEX Classroom Resources

   View Standards     Standard(s): [MA2015] AL2 (9-12) 7 :

7 ) (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. (Use technology to approximate roots.) [N-VM6] (Alabama)

[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] ALT (9-12) 7 :

7 ) (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. (Use technology to approximate roots.) [N-VM6] (Alabama)

[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]

In Module 2, Topic A, students look at incidence relationships in networks and encode information about them via high-dimensional matrices. Questions on counting routes, the results of combining networks, payoffs, and other applications, provide context and use for matrix manipulations:  matrix addition and subtraction, matrix product, and multiplication of matrices by scalars.

Note: Although this module is identified as Precalculus and Advanced Topics in the EngageNY curriculum, it corresponds to the Algebra II and Algebra II with Trigonometry Alabama Courses 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) 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.