Vector and Matrix Quantities

PC.NVMQ.1Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes.PC.NVMQ.10Multiply a vector by a matrix of appropriate dimension to produce another vector. Work with matrices as transformations of vectors.PC.NVMQ.11Apply 2×2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.PC.NVMQ.2Represent and model with vector quantities. Use the coordinates of an initial point and of a terminal point to find the components of a vector.PC.NVMQ.3Represent and model with vector quantities. Solve problems involving velocity and other quantities that can be represented by vectors.PC.NVMQ.4Perform operations on vectors.PC.NVMQ.4aAdd and subtract vectors using components of the vectors and graphically.PC.NVMQ.4bGiven the magnitude and direction of two vectors, determine the magnitude of their sum and of their difference.PC.NVMQ.5Multiply a vector by a scalar, representing the multiplication graphically and computing the magnitude of the scalar multiple.PC.NVMQ.6Use matrices to represent and manipulate data. (Note: This Graduation Standard is covered in Grade 8.)PC.NVMQ.7Perform operations with matrices of appropriate dimensions including addition, subtraction, and scalar multiplication.PC.NVMQ.8Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.PC.NVMQ.9Understand 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.
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