# Common Core: Vector & Matrix Quantities

##### 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, 2018##### HSN.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, 2018##### HSN.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, 2018##### HSN.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, 2018##### HSN.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, 2018##### HSN.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, 2018##### HSN.VM.C6

(+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.

October 1, 2018##### HSN.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, 2018##### HSN.VM.A1

(+) 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).

October 1, 2018##### HSN.VM.B4c

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.

October 1, 2018