N.VM.C: Perform operations on matrices and use matrices in applications.

Perform operations on matrices and use matrices in applications.

N.VM.C.6Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.N.VM.C.7Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.N.VM.C.8Add, subtract, and multiply matrices of appropriate dimensions.N.VM.C.9Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.N.VM.C.10Understand 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.VM.C.11Multiply 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.VM.C.12Work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.

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