High School: Number and Quantity
HSN.VM.C12
(+) Work with 2 x 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.
October 1, 2018HSN.VM.B5a
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).
October 1, 2018HSN.VM.B5b
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).
October 1, 2018HSN.VM.C6
(+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
October 1, 2018HSN.VM.C7
(+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
October 1, 2018HSN.VM.C9
(+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
October 1, 2018HSN.VM.C10
(+) 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.
October 1, 2018HSN.VM.C11
(+) 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.
October 1, 2018HSN.CN.B4
(+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.
October 1, 2018HSN.VM.B4a
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.
October 1, 2018HSN.CN.B5
(+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (-1 + √3 i)3 = 8 because (-1 + √3 i) has modulus 2 and argument 120°.
October 1, 2018