N-VM. Vector and Matrix Quantities

N-VM.A. Represent and model with vector quantities.

N-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., $\textbf{v}$, $|\textbf{v}|$, $||\textbf{v}||$, $v$).

• No tasks yet illustrate this standard.

N-VM.A.2. Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

• No tasks yet illustrate this standard.

N-VM.A.3. Solve problems involving velocity and other quantities that can be represented by vectors.

• No tasks yet illustrate this standard.

N-VM.B. Perform operations on vectors.

N-VM.B.4. Add and subtract vectors.

• No tasks yet illustrate this standard.

N-VM.B.4.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.

• No tasks yet illustrate this standard.

N-VM.B.4.b. Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

• No tasks yet illustrate this standard.

N-VM.B.4.c. Understand vector subtraction $\textbf{v} - \textbf{w}$ as $\textbf{v} + (-\textbf{w})$, where $-\textbf{w}$ is the additive inverse of $\textbf{w}$, with the same magnitude as $\textbf{w}$ and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.

• No tasks yet illustrate this standard.

N-VM.B.5. Multiply a vector by a scalar.

• No tasks yet illustrate this standard.

N-VM.B.5.a. Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as $c(v_x, v_y) = (cv_x, cv_y)$.

• No tasks yet illustrate this standard.

N-VM.B.5.b. Compute the magnitude of a scalar multiple $c\textbf{v}$ using $||c\textbf{v}|| = |c|v$. Compute the direction of $c\textbf{v}$ knowing that when $|c|{v} \neq 0$, the direction of $c\textbf{v}$ is either along $\textbf{v}$ (for $c > 0$) or against $\textbf{v}$ (for $c < 0$).

• No tasks yet illustrate this standard.

N-VM.C. Perform operations on matrices and use matrices in applications.

N-VM.C.6. Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.

• No tasks yet illustrate this standard.

N-VM.C.7. Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.

• No tasks yet illustrate this standard.

N-VM.C.8. Add, subtract, and multiply matrices of appropriate dimensions.

• No tasks yet illustrate this standard.

N-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.

• No tasks yet illustrate this standard.

N-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.

• No tasks yet illustrate this standard.

N-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.

• No tasks yet illustrate this standard.

N-VM.C.12. Work with $2 \times2$ matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.

• No tasks yet illustrate this standard.