Vector & Matrix Quantities
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Represent And Model With Vector Quantities.
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N.VM.1(+) Recognize vector quantities as h…more
(+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).
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N.VM.2(+) Find the components of a vector …more
(+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
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N.VM.3(+) Solve problems involving velocit…more
(+) Solve problems involving velocity and other quantities that can be represented by vectors.
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Perform Operations On Vectors.
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N.VM.4(+) Add and subtract vectors.…more
(+) Add and subtract vectors.
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N.VM.4.aAdd vectors end-to-end, component-wi…more
Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.
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N.VM.4.bGiven two vectors in magnitude and d…more
Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
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N.VM.4.cUnderstand vector subtraction v – …more
Understand vector subtraction v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.
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N.VM.5(+) Multiply a vector by a scalar.…more
(+) Multiply a vector by a scalar.
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N.VM.5.aRepresent scalar multiplication grap…more
Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).
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N.VM.5.bCompute the magnitude of a scalar mu…more
Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).
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Perform Operations On Matrices And Use Matrices In Applications.
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N.VM.6(+) Use matrices to represent and ma…more
(+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
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N.VM.7(+) Multiply matrices by scalars to …more
(+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
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N.VM.8(+) Add, subtract, and multiply matr…more
(+) Add, subtract, and multiply matrices of appropriate dimensions.
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N.VM.9(+) Understand that, unlike multipli…more
(+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
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N.VM.10(+) Understand that the zero and ide…more
(+) 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.
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N.VM.11(+) Multiply a vector (regarded as a…more
(+) 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.
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N.VM.12(+) Work with 2 × 2 matrices as tra…more
(+) Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.
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