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STANDARDS

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US-SC

Math

South Carolina Math

Pre-Calculus: Vector and Matrix Quantities

PC.NVMQ.1

Fully covered
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.

PC.NVMQ.2

Fully covered
Represent and model with vector quantities. Use the coordinates of an initial point and of a terminal point to find the components of a vector.

PC.NVMQ.3

Fully covered
Represent and model with vector quantities. Solve problems involving velocity and other quantities that can be represented by vectors.

PC.NVMQ.4

Perform operations on vectors.

PC.NVMQ.4a

Fully covered
Add and subtract vectors using components of the vectors and graphically.

PC.NVMQ.4b

Fully covered
Given the magnitude and direction of two vectors, determine the magnitude of their sum and of their difference.

PC.NVMQ.5

Fully covered
Multiply a vector by a scalar, representing the multiplication graphically and computing the magnitude of the scalar multiple.

PC.NVMQ.6

Not covered
Use matrices to represent and manipulate data. (Note: This Graduation Standard is covered in Grade 8.)
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PC.NVMQ.7

Fully covered
Perform operations with matrices of appropriate dimensions including addition, subtraction, and scalar multiplication.
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PC.NVMQ.8

Not covered
Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
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PC.NVMQ.9

Mostly covered
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.
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PC.NVMQ.10

Fully covered
Multiply a vector by a matrix of appropriate dimension to produce another vector. Work with matrices as transformations of vectors.
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PC.NVMQ.11

Not covered
Apply 2×2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.
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