Precalculus and Advanced Topics Module 2, Topic B, Overview

Topic B explores the geometric context for higher-dimensional matrices.  The geometric effect of matrix operations—matrix product, matrix sum, and scalar multiplication—are examined, and students come to see, geometrically, that matrix multiplication for square matrices is not a commutative operation, but that it still satisfies the associative and distributive properties.  The geometric and arithmetic roles of the zero matrix and identity matrix are discussed, and students see that a multiplicative inverse to a square matrix exists precisely when the determinant of the matrix is non-zero.

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Common Core Learning Standards

CCLS State Standard
N.VM.7 (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a...
N.VM.8 (+) Add, subtract, and multiply matrices of appropriate dimensions.
N.VM.9 (+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is...

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