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Основно съдържание

STANDARDS

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US-AR

Math

Arkansas Math

Algebra III: Matrix Operations

Students will perform operations with matrices and use them to solve systems of equations.

MO.1.AIII.1

Not covered
Use matrices to represent and manipulate data (e.g., to represent payoffs or incidence relationships in a network)
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MO.1.AIII.2

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

MO.1.AIII.3

Mostly covered
Add, subtract, and multiply matrices of appropriate dimensions

MO.1.AIII.4

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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MO.1.AIII.5

Partially 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

MO.1.AIII.6

Fully covered
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

MO.1.AIII.7

Not covered
Work with 2 X 2 matrices as transformations of the plane; interpret the absolute value of the determinant in terms of area
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MO.1.AIII.8

Fully covered
Represent a system of linear equations as a single matrix equation in a vector variable

MO.1.AIII.9

Fully covered
Find the inverse of a matrix if it exists; use the inverse to solve systems of linear equations using technology for matrices of dimension 3 X 3 or greater