12-2 MATRIX MULTIPLICATION MULTIPLY MATRICES BY USING SCALAR AND MATRIX MULTIPLICATION.

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Presentation transcript:

12-2 MATRIX MULTIPLICATION MULTIPLY MATRICES BY USING SCALAR AND MATRIX MULTIPLICATION.

SCALAR MULTIPLICATION

PRACTICE

PROPERTIES OF SCALAR MULTIPLICATION

SOLVING A MATRIX EQUATION WITH SCALARS

MATRIX MULTIPLICATION

APPLYING TDFGSPAT Washington10109 New York6005

PROPERTIES OF MATRIX MULTIPLICATION  Dimensions: if A is m x n and B is n x p, then AB will be m x p  A product will not exist if the number of columns in A does not match the number of rows in B  (3 x 2)(2 x 4) product exists (2 x 4)(3 x 2) product does not exist  Assume A, B, and C are n x n matrices and O is the zero matrix  Closure Property: AB is an n x n matrix  Associative Property of Multiplication: (AB)C = A(BC)  Distributive Property: A(B + C) = AB + AC and (B + C)A = BA + CA  Multiplicative Property of Zero: OA = AO = O

ASSIGNMENT  Odds p.777 #7-35,44