MO.1.AIII

MO.1.AIII

MO.1.AIII.1Use matrices to represent and manipulate data (e.g., to represent payoffs or incidence relationships in a network)MO.1.AIII.2Multiply matrices by scalars to produce new matrices (e.g., as when all of the payoffs in a game are doubled)MO.1.AIII.3Add, subtract, and multiply matrices of appropriate dimensionsMO.1.AIII.4Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive propertiesMO.1.AIII.5Understand 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 inverseMO.1.AIII.6Multiply 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 vectorsMO.1.AIII.7Work with 2 X 2 matrices as transformations of the plane; interpret the absolute value of the determinant in terms of areaMO.1.AIII.8Represent a system of linear equations as a single matrix equation in a vector variableMO.1.AIII.9Find the inverse of a matrix if it exists; use the inverse to solve systems of linear equations using technology for matrices of dimension 3 X 3 or greater
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