HS Math Concept: Vector and Matrix Quantities


Vector and Matrix Quantities


Represent and model with vector quantities.
HSN-VM.A.1. (+) 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). tools-icon
HSN-VM.A.2. (+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. tools-icon
HSN-VM.A.3. (+) Solve problems involving velocity and other quantities that can be represented by vectors.  tools-icon
Perform operations on vectors.
HSN-VM.B.4. (+) Add and subtract vectors.  tools-icon
a. 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.  tools-icon
b. Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.  tools-icon
c. 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.  tools-icon
HSN-VM.B.5. (+) Multiply a vector by a scalar.  tools-icon
a. 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).  tools-icon
b. 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).  tools-icon
Perform operations on matrices and use matrices in applications.
HSN-VM.C.6. (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.  tools-icon
HSN-VM.C.7. (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.  tools-icon
HSN-VM.C.8. (+) Add, subtract, and multiply matrices of appropriate dimensions.  tools-icon
HSN-VM.C.9. (+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.  tools-icon
HSN-VM.C.10. (+) 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.  tools-icon
HSN-VM.C.11. (+) 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.  tools-icon
HSN-VM.C.12. (+) Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.  tools-icon