MATRIX MULTIPLICATION

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Presentation transcript:

MATRIX MULTIPLICATION MATRICES MATRIX MULTIPLICATION

Matrix Multiplication If A, B, and C are matrices and k is an integer, then matrix multiplication is: Associative: A(BC) = (AB)C Left Distributive: A(B+C) = AB+BC Right Distributive: (A+B)C=AC +BC Associative with Scalar Multiplication: k(AB) = (kA)B = A(kB) It is not commutative: AB ≠ BA

Matrix Multiplication You can multiply matrices only if the number of columns in the first matrix equals the number of rows in the second matrix. 2 columns 2 rows

Matrix Multiplication Notice the dimensions of the matrices and their product. Note that if it had been a 2x3●3x2, the result would have been a 2x2 matrix. Commutative does not work! 3 x 2 2 x 3 3 x 3 __ __ __ __

State Whether the Product is Defined for Matrices A and B A: 3X6, B:6x2 AB is a 3x2 matrix and is defined! A: 2X7, B: 1X7 AB is not defined! A: 4X2, B: 2X5 AB is a 4x5 matrix and is defined!

Matrix Multiplication So how do we multiply a matrix? With a math note sheet telling us how! Please write this down! 

Example

Matrix Multiplication

Matrix Multiplication Another example: 3 x 2 2 x 1 3 x 1

Example

Continued…

Real Life Problem---Soccer Two soccer teams submit equipment lists for the season as shown: How much will the total equipment cost for each team? Quick Goals Costs Uniforms Balls Balls JV Quick Goals Quick Goals Varsity Uniforms

Real Life Problem---Soccer