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- Common Core MathK - 8High School

# Number and Quantity: Vector and Matrix Quantities

517 questions26 skills

# Number and Quantity: Vector and Matrix Quantities

517 questions26 skills

## HSN-VM.A.1

36 questions2 skills

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*).## HSN-VM.A.2

30 questions1 skill

Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

## HSN-VM.A.3

12 questions1 skill

Solve problems involving velocity and other quantities that can be represented by vectors.

## HSN-VM.B.4

56 questions3 skills

Add and subtract vectors.

## HSN-VM.B.4a

86 questions4 skills

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.

## HSN-VM.B.4b

96 questions5 skills

Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

## HSN-VM.B.4c

40 questions2 skills

Understand vector subtraction

**–***v***as***w***+ (–***v***), 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.***w*## HSN-VM.B.5

40 questions2 skills

Multiply a vector by a scalar.

## HSN-VM.B.5a

46 questions2 skills

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}).## HSN-VM.B.5b

20 questions1 skill

Compute the magnitude of a scalar multiple

*c***using ||***v**c***|| = |***v**c*|**. Compute the direction of***v**c***knowing that when |***v**c*|**≠ 0, the direction of***v**c***is either along***v***(for***v**c*> 0) or against**(for***v**c*< 0).## HSN-VM.C.6

20 questions1 skill

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

## HSN-VM.C.7

36 questions2 skills

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

## HSN-VM.C.8

124 questions6 skills

Add, subtract, and multiply matrices of appropriate dimensions.

Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.

Skills for this standard are coming soon.

## HSN-VM.C.10

30 questions1 skill

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.

## HSN-VM.C.11

28 questions2 skills

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.

## HSN-VM.C.12

31 questions2 skills

Work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.